This study investigates the issue of stabilisation to input-to-state stability (ISS) by event-triggered impulsive control (ETIC) for continuous-time dynamical systems (CDSs) with external inputs/disturbances. The CDSs are more general systems with possible multiple vector fields and dynamics. The ETIC scheme is based on three key indices: threshold value, control-free index, and check period, and it is executed by designing three levels of events from which ETIC is triggered. Both ETIC and ETIC with time-delays (delayed ETIC) are studied, respectively, and the criteria for ISS are derived for CDSs under ETIC. Thus the stabilisation to ISS is achieved for CDSs by the designed ETIC with or without time delays. The data dropout of ETIC is also investigated, where the maximal allowable dropout rates are estimated, respectively. It shows that the proposed ETIC scheme has advantages over the reported event-triggered control and has robustness with respect to the network-induced time-delays although larger time-delays might lead to a slower convergence speed for the stabilisation to ISS. Finally, two examples with numerical simulations are given to illustrate the obtained results.

This study investigates the bipartite output containment control of general linear heterogeneous multi-agent systems on signed communication networks with antagonistic interactions, modelled as negative weights on the digraph. The authors first formulate a new control problem referred to as the bipartite output containment. This control paradigm aims to make each follower's output converge to a dynamic convex hull spanned by the outputs and the sign-inverted outputs of multiple leaders. Second, the authors prove that the bipartite output containment problem can be solved by making some suitably defined signed output containment errors go to zero asymptotically. Then, the authors construct three different control protocols, using full-state feedback, static output-feedback, and dynamic output-feedback designs. These control protocols are based on a distributed feed-forward approach, which requires a feedback gain to make the closed-loop system matrix stable, and a feed-forward gain to drive trajectories of the closed-loop system toward a subspace that renders the regulated signed output containment errors zero. Numerical simulations are performed to validate the proposed control protocols.

This study investigates the synchronisation problem for complex dynamical networks with non-linear coupling via state-dependent impulsive control. In contrast to most existing publications, impulses occurring are not at fixed instants but depend on the states of each node. Based on the differential mean value theorem and inequality techniques, several sufficient conditions with theoretical demonstration ensuring every solution of the error nodes intersect each surface of the discontinuity exactly once are derived. Moreover, by applying the B-equivalence method, the error system with state-dependent impulses can be reduced to the fixed-time impulsive ones, which can be analysed via Lyapunov stability theory and mathematical induction. Finally, two numerical examples are carried out to demonstrate the performance of the obtained results.

In this study, the authors propose a novel distributed continuous-time algorithm based on projection and gradient to solve the optimisation problem of a multi-agent system under any initialisation manner over a directed graph. The considered cost function is a summation of all local cost functions with local constraints set. The point of the proposed protocol is that a new scheme is proposed to offset the non-zero local gradients of local cost functions at the minimiser. The optimal solution of the proposed algorithm is shown using the variational inequality under some conditions. Moreover, exponential convergence rate of the designed algorithm is verified with the help of the identity transformation and Lypaunov stability theory. Finally, a numerical example and a comparison are provided to demonstrate the effectiveness of the theoretical results obtained.

The moment exponential input-to-state stability (ISS) problem for a class of non-linear switched stochastic systems is studied. A continuously differentiable Lyapunov function with indefinite derivative is introduced, which generalises classic Lyapunov function method. Two situations are considered: (i) synchronous switching, i.e. candidate controllers coincide with system modes; (ii) asynchronous switching, i.e. the candidate controllers have a lag to the switching of the system modes. By employing indefinite derivative Lyapunov function method and average dwell-time approach, sufficient conditions for moment exponential ISS of the systems are derived. Finally, an example is given to illustrate the effectiveness of the authors' results.

The aim of the article is to design a chattering free robust adaptive integral higher order sliding mode control for load frequency problems in multi-area hydro power systems using decentralised variable structure control methodology. The proposed controller assures change in frequency in all the areas due to load disturbance converge to zero in finite time. Results are compared with the performances obtained using integral sliding mode control (ISMC) and integral higher order sliding mode control (IHOSMC). The proposed controller helps in achieving finite time convergence of change in frequency due to load disturbances with chattering free and smooth control signal as compared to that obtained using ISMC and IHOSMC. Performance of the controller is tested for plant considered with non-linearities in power system such as generation rate constraints and governor deadband. The proposed controller is also validated against random load disturbances and IEEE large bus system (39-bus system).

In this study, the authors present a robust trajectory tracking control for a class of uncertain Euler–Lagrange (EL) systems using event-triggered-based sliding mode strategy. Here, the sliding mode-based tracking control is designed to ensure the robust stability of EL systems in the presence of external disturbances/uncertainties. Unlike periodic implementation, in event-triggering strategy, the control signal is updated on demand subject to system stability, so the frequent periodic execution of control tasks is avoided. Here, the event-triggered implementation of the sliding mode-based tracking control achieves the robust stability with desired steady-state performance and reduced computations of control. To realise this, sufficient conditions are derived using Lyapunov analysis such that the proposed controller yields desired tracking performance. It is shown that the triggering condition proposed here ensures Zeno free execution of triggering sequence. Finally, the theoretical development of the study is illustrated through numerical simulation on a two-link robotic manipulator.

This study deals with designing a robust fixed-order dynamic output feedback controller for uncertain fractional-order linear time-invariant systems by means of linear matrix inequalities (LMIs). The authors’ purpose is to design a low-order controller that stabilises the fractional-order linear system in the presence of model uncertainties. No limiting constraint on the state space matrices of the uncertain system is assumed in the design procedure. Furthermore, adopting the most complete model of linear controller, with direct feedthrough parameter, does not disturb the LMI-based approach of developing robust stabilising control. Eventually, the authors illustrate the advantages of the proposed method by some examples and their numerical simulation.

This study considers a model that a centralised sensor network is attacked by an invader, who launches the denial-of-service (DoS) attack on the network. To understand the behaviour of the invader and propose necessary protection accordingly, the authors study how the invader optimises his attack. In the model, the sensors take a measurement of a process and send the measurements to a remote estimator for state estimation. The invader intends to block the communication channels from the sensors to the estimator by the DoS attack in order to degrade the estimation performance. Constrained by a power budget, the invader needs to decide which sensors and at which time instances to attack, with the target that the estimation performance is mostly deteriorated. In this study, two scenarios that the system has a single sensor and has multiple sensors are investigated, respectively. For the system with a single sensor, the analytical result of the optimal attack schedules is given. For the system with multiple sensors, numerical methods are proposed, where the problem is relaxed and transformed into a convex optimisation problem which can be solved by efficient numerical algorithms.

This study considers the optimal linear estimation problem for the discrete-time stochastic fractional-order system in its more general formulation. The system is allowed to be in singular form, rectangular, with dynamical and measurement noises correlated. First, some new conditions for the solvability, regularity and causality to discrete-time linear stochastic fractional-order singular (FOS) systems are given, and then, a new Kalman filter (KF) fractional singular KF (FSKF) is designed for such systems. This general form of filter is derived using deterministic arguments in a completely self-contained way besides the stochastic reasoning and covers the nominal singular and fractional KFs. Instead of the standard stochastic formulation, the filter recursions are obtained as a solution of a convenient organisation of the deterministic data-fitting estimate of an entire state trajectory given the measurements for both time-invariant and time-varying cases. To present the efficiency of the proposed algorithm, results of numerical simulations are presented.

This study presents a systematic procedure to solve the problem of finite-time distributed global optimal control for the leaderless and leader-follower homogeneous multi-agent systems (MASs). Each agent's dynamics is given in general form of continuous-time linear time-varying (LTV) systems. The communication network among the agents is also assumed to be undirected and directed under fixed topology. First, based on asymptotic stability principle, inverse optimal results of general LTV systems are constructed. Second, the necessary and sufficient conditions are given for the existence of the distributed optimal state feedback and optimal dynamic output feedback control that solves a global optimal control problem for MASs. Then, the sufficient condition for finite-time stability of both the state and the output feedback problems for MASs are stated. Finally, some numerical example results are provided to illustrate the effectiveness and applicability of the proposed scheme.

Robust backstepping control of non-linear systems with derivation orders (commensurate or non-commensurate) lying at interval (0, 2) is proposed in this study. The stability and robustness properties are proved using a linearisation procedure in contrast to the classic recursive Lyapunov approach to backstepping. Vector, adaptive and robustness extensions are then developed to solve general tracking and stabilisation control problems. The adaptive extension is proved with a non-Lyapunov approach based on inequalities on non-negative fractional integrals. The mixed-order nature enables to control integer order systems using fractional operators. Through simulations, it is shown that the performance of the controllers depends on their derivation orders. In particular, for transient behaviour and the root mean square value of the control signal, the fractional controllers proposed exhibit improved responses as compared with the integer ones.

A fuzzy approach to the optimal control design for a kind of uncertain flexible joint manipulator is proposed. The system contains mismatched uncertainty which is described by fuzzy set theory and is assumed to be bounded. By implanting a fictitious control and transforming the system with new state variables, an adaptive robust controller is designed to guarantee the uniform boundedness and uniform ultimate boundedness of the transformed system. The proposed control is only based on the existence of the uncertainty bound and is not if–then heuristic rules-based. Furthermore, the performance of the original system is also proven theoretically. By applying D-operation, the optimal design problem associated with the control can then be solved by minimising a constrained performance index. The performance index, which is based on the fuzzy information, includes average fuzzy system performance and control effort. The resulting control design is systematic and is able to assure the deterministic performance as well as the fuzzy performance. An illustrative example is given to demonstrate the authors' conclusions.

This work addresses the problem of the estimator design for the periodic neural networks with polytopic uncertain connection weight matrices. The polytopic uncertainty is used to model the uncertain weight matrices. Bernoulli processes are employed to characterise the randomly occurred sensor nonlinearities, where the sensors are distributed in a large area. A Lyapunov function which depends both on the polytopic vertices and the period is constructed to improve the performance of the estimator. Sufficient conditions of the stochastic stability with performance for the augmented system are established, and the corresponding gains of the estimator are designed. Finally, an illustrative numerical example is given.

This study proposes an intelligent digital redesign (IDR) technique for sampled-data fuzzy filters of non-linear systems. The technique constructs a closed-loop system with predesigned continuous-time and sampled-data filters based on the Takagi–Sugeno (T–S) fuzzy model. The closed-loop systems ensure asymptotic stability and state-matching condition in the IDR problem. Unlike previous techniques, the proposed method solves the IDR problem without a discretization process which degrades the IDR performance. Sufficient conditions for solving the IDR problem are proposed and derived in terms of linear matrix inequalities. In addition, the performance recovery of the sampled-data fuzzy filter is shown. Finally, the feasibility of the proposed technique is demonstrated in two simulation examples.

This study addresses the problem of robust exponential stability and stabilisation of sampled-data linear parameter varying (LPV) systems with an aperiodic sampling rate. Utilising the input delay approach and taking the distance between real and measured parameters into account, new stability and stabilisation conditions are derived for LPV systems with arbitrary dependence on the parameters. By means of a modified parameter dependent Lyapunov–Krasovskii functional, stability conditions are formulated as a set of parameter-dependent linear matrix inequalities (PLMIs) which are suitable to investigate the effect of the sampling rate on the closed-loop stability. Furthermore, sufficient conditions to guarantee the feasibility of PLMIs over the set of whole parameters are derived that lead to the feasibility of a finite number of linear matrix inequalities. Applying the projection lemma new stability analysis conditions are obtained and shown to be suitable for the stabilisation problem. Under the new stability criteria, an efficient procedure developed for robust sampled-data controller design in the presence of uncertainty on the varying parameters and unknown time varying sampling rate. The proposed method is applied to a sampled-data fuzzy control problem of a non-linear system and multi-rate sampled-data LPV systems. Several examples show the efficiency of the method.

Self-excited milling vibrations represent an important problem in the manufacturing industry. This study presents an out-of-process analysis based on the Lyapunov–Krasovskii approach which provides operational guidelines for the proper selection of the cutting parameters to guarantee a stable vibration-free process. The proposed approach considers a time-delay two degree of freedom model and takes advantage of some useful tools of the control theory developed for time-delay systems such as the descriptor method and the Bessel–Legendre inequalities.

This study addresses the containment control problem for high-order multi-agent systems with heterogeneous time delays. Here the authors consider two cases: the leaders are stationary and the leaders are dynamic. Based on the distributed containment control protocols with proper gain parameters, they utilise the properties of the product of infinite matrices to derive some sufficient conditions. The obtained results guarantee that all the followers can asymptotically converge to a convex hull spanned by those of the leaders under the proper gain parameters if the communication topology contains a directed spanning forest rooted at the leaders. Finally, some numerical simulations are presented to illustrate the effectiveness of their theoretical results.

Many mechanical systems can be modelled by vector second-order differential equations. In this study, the observation problem of a class of vector second-order Lipschitz non-linear systems with discrete measurements is addressed. Under the premise that the discrete measurements of position and velocity vectors are available, an impulsive observer in the second-order framework is designed. The proposed observation scheme ensures that the second-order structure of the observed system can be retained, and allows the sampling on the system output to be aperiodic. The stability analysis of the observation error system is performed by employing an impulse-time-dependent discretised Lyapunov function based method. The novelty of the introduced Lyapunov function is that its structure relies on the partition on the impulse intervals. With the increase of the partition number, the existence condition of impulsive natural observers can be relaxed. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method.

In this study, a novel distributed event-triggered scheme (ETS) using only triggered information is presented to solve the problem of the leader-following consensus for a class of multi-agent systems with general linear dynamics under fixed and switching topologies. First, the novel triggering conditions are proposed for fixed topology by virtue of discrete communications between neighbouring agents at the triggering times, which eliminates continuous inter-agent communication and reduces the frequency of controller update simultaneously. Second, for switching topology including both graphs that have directed spanning tree and graphs that do not, the authors propose the topology-dependent distributed ETS to guarantee consensus by an average dwell time approach. Noteworthily, Zeno behaviour of triggering time sequences is excluded under fixed and switching topologies. Examples validate the effectiveness and show the advantage of the proposed ETS by comparison.