The design and validation of a new fractional order (FO) reaching law for uncertain discrete-time systems is studied. A sliding mode controller is subsequently constructed by adopting this law. Unlike previous works, the presented reaching law is established on the basis of the Grünwald–Letnikow FO calculus of the switching function. A high-order disturbance compensator is integrated into this reaching law to evaluate and compensate the disturbance. A rigorous theoretical analysis is given to demonstrate the superior performance of the reaching law. Results indicate that the developed method owns the ability to guarantee an O(T^{n +1}) order ultimate magnitude of the quasi-sliding mode domain. Therefore, the presented method is capable of further mitigating chattering and guaranteeing a further improvement on the control accuracy in comparison with previous reaching law methods. Moreover, sliding mode dynamics of the discrete-time system in and out the vicinities of the sliding surface is analysed in detail. Simulation results are presented to verify the feasibility and effectiveness of the developed method.

In this study, for the first time, a stabilisation criterion is derived for the TCP/AQM system with time-varying delay and finite-frequency (FF) specifications. Two important results are established. The first one shows that the TCP/AQM system operates on a frequency domain. The second one introduces a new model transformation of linear systems with time-varying delay. The objective is to alleviate the impact that buffering has on latency-sensitive traffic while preserving bulk throughput performance. Standing on the new model transformation, the scaled small-gain theorem and the theory, the authors suggest new conditions expressed in terms of linear matrix inequalities for designing powerful Active Queue Management. Finally, the engineering relevance of the theory has been evaluated with different realistic scenarios in NS3 and shows that FFAQM scheme provides the best quality of service.

This study investigates the filter design problem for two-dimensional (2D) discrete-time non-linear systems in Takagi–Sugeno (T–S) fuzzy model. The frequency of the exogenous disturbances is assumed to belong to a known finite frequency (FF) domain. An FF performance is defined for 2D discrete-time systems, which generalises the standard one and makes use of the frequency-domain characteristics of practical signals. By virtue of the defined FF performance, sufficient conditions are proposed for analysing the disturbance attenuation performance of the filtering error system. Efficient conditions are obtained to guarantee the existence of a filter and such that the error system is asymptotically stable with an FF performance index. A systematic filter design scheme is developed by converting the corresponding fuzzy filter design into a convex optimisation problem. Finally, a gas absorption system is employed to illustrate the validity of the proposed methods.

This work proposes a mathematical solution for plants with full set of uncertain parameters which is based on the active disturbance rejection control method. This method has been studied for three decades and its main characteristic is the use of an extended state observer to estimate the non-measurable signals of the plant. However, the application of the basic methodology requires the exact knowledge of the system control gain, which is difficult to measure in the case of parametric uncertainties. Recently, some advances have been discussed in the literature. Some results have revealed the capability of them of rejecting the unknown input disturbance and of ensuring the stability of closed-loop transfer functions, even in the case of unknown order and/or relative degrees. However, such proposals have not been effective for large level of parametric uncertainties. The idea of the present work is to relax the requirement of exact knowledge of plant parameters by proposing modifications in the control structure. Mathematical analysis show that the proposed modification does not affect the original purpose of output tracking. The performance of the proposed strategy is compared with other schemes by using numerical simulations. In addition, experimental results on a real cart-pendulum system are presented.

The authors interest in this work is to perform a precise real-time flocking of multiple unmanned aerial vehicles (UAVs). A consensus-based flocking algorithm that ensures a precise security distance between UAVs is proposed. By using Lyapunov theoretical analysis, the authors propose a flocking algorithm that ensures the ultimate boundedness of multiple-UAV system solutions. Moreover, this algorithm is enhanced by a distributed integral control that renders the inter-distances between UAVs more precise. Finally, experimental results are provided to prove and show the efficiency of these algorithms.

The authors investigate the problem of state estimation for stochastic hybrid dynamical systems with state equality constraints. They divided this problem into three categories depending on the linearity or non-linearity of equality constraints as well as on the dependence of constraints on the operating mode. For the mode-independent equality-constrained linear case, they present sufficient conditions on process dynamics and filter initial conditions so that the classical interacting multiple model (IMM) algorithm yields state estimates satisfying the linear equality constraint for all subsequent times. For both linear and non-linear systems, the mode-dependent equality constraints must be enforced over time by the filter. They present a modified version of the IMM filter to enforce the equality constraints in such cases. Their numerical results show that the proposed methods provide more accurate estimates than the IMM unconstrained estimates.

This study considers an optimal output anti-synchronisation problem for linear multi-agent systems with non-identical dynamics and antagonistic interactions. It is assumed that the agents are non-introspective, i.e. they cannot get their own states or outputs, and can only get a linear combination of relative outputs in the neighbourhood. First, a state transformation is made, which aims at reducing the dimension of the model underlying the output anti-synchronisation errors by removing redundant modes that have no effect on the output anti-synchronisation errors. Then, optimal state feedback controllers are proposed for agents to realise the output anti-synchronisation by constructing discounted performance functions and by solving the discounted algebraic Riccati equation. Moreover, by using an iterative technique, an offline algorithm is provided to solve the linear quadratic tracking problem. In addition, a distributed node-based adaptive observer is proposed to produce an estimate of the state with only relative output information of neighbouring agents by utilising a high-gain approach. The convergence of the proposed adaptive observer is analysed with the help of a Lyapunov function method. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed approach.

In this study, the consensus problem is investigated for the multi-agent systems with antagonistic interactions and communication delay under the event-triggered control protocol. For the directed signed networks, an event-based interaction protocol is first proposed. Then it is shown that with the proposed protocol, bipartite consensus can be realised for the structurally balanced signed networks with distributed communication delay. As for the structurally unbalanced signed networks with communication delay, it is proved that consensus can also be reached under the proposed event-triggered scheme and the final consensus value is zero. It should be emphasised that the proposed event-triggered controllers depend only on the local information. Furthermore, Zero phenomenon can be excluded, and the positive lower bound of the inter-event times is simultaneously provided. Finally, the effectiveness of proposed event-triggered schemes is demonstrated by one numerical example.

In this study, stabilisation of input-delay non-linear systems in the presence of disturbance based on prediction variable is studied. For both disturbance estimation and delay compensation, an extended prediction variable as well as adaptive sliding mode controller are proposed in which the open-loop system is not required to be stable. In the proposed prediction variable one needs to estimate disturbance in the future. In order to solve this problem a new non-linear disturbance observer (NDOB) is proposed. Considering the NDOB in the closed-loop system, the stability analysis of error dynamic is performed. And the asymptotic stability of non-linear system with input delay is guaranteed for some class of disturbance. Simulation results finally validate the good performance and robustness of the proposed controller based on disturbance observer.

The main intention of this study is to design the fuzzy impulsive observer-based output controller scheme for hybrid Takagi–Sugeno (T–S) fuzzy permanent magnet synchronous generator (PMSG) model. Initially, the non-linearities of the PMSG differential model is equivalently transformed into linear sub-models via T–S fuzzy approach. Then, the theoretical sufficient conditions are derived by utilising the Lyapunov stability theory. Distinct to the existing studies, the overall contributions of the present work is summarised as follows: (i) the paper proposes the impulsive controller, which is a combination of both continuous and discontinuous factors that can handle the uncertainties in a complex T–S fuzzy PMSG model. (ii) The time-dependent Lyapunov functional (based on parallel distributed compensation method) has introduced for the given model, and then the sufficient conditions are proposed as solvable linear matrix inequalities. The simulation concerning the industrial problem of PMSG model is validated with the proposed theoretical conditions that guarantee the global asymptotic stability performance of the chaotic model.

The containment problem of heterogeneous multi-agent systems with fixed time delay under directed network is considered for both continuous-time and discrete-time multi-agent systems. Leaders and followers have different dynamics, modelled by double-integrator and single-integrator, respectively. It is also assumed that all leaders are stationary. Unlike the current approach in the literature which utilises LMIs to derive sufficient condition for containment reaching, the authors employ Laplace transform/Z-transform and final value theorem to obtain the necessary and sufficient condition which guarantees the containment of follower agents in the presence of communication delays. This approach gives the exact maximum allowed time delay, which is larger than the bound obtained by previous approaches. This study also proposes a noble reduced-order dynamic method, by adding virtual agents, in order to use final value theorem for stability analysis in the presence of heterogeneity in the network. In the end, to illustrate the effectiveness of the theoretical results, simulation examples are provided.

This study deals with the problem of relative motion control with 6 degrees of freedom (6DOF) for spacecrafts without a priori knowledge of the inertia parameters. Considering the system natural couplings, the integrated rotational and translational dynamics of the spacecraft are achieved. By a series of first-order filter operations, an expression of the parameter estimation error is derived and then used for the design of an integrated finite-time tracking controller applying adaptive backstepping technique. Proven by the Lyapunov theory, the proposed controller can guarantee that the errors of trajectory tracking and parameter identification simultaneously converge to zero in finite time. Furthermore, to be applied in practice, the controller is adapted for the spacecraft subject to external disturbance and input saturation. Compared with the previous control designs, the proposed control strategy can realise inertia parameter identification together with tracking of command position and attitude in finite time, in the presence of input saturation and external disturbance. The effectiveness of the control law is finally demonstrated by numerical simulations.

This study concentrates on the parameter estimation of multivariate pseudo-linear autoregressive moving average systems by means of the multi-innovation identification theory and data filtering technique. A multi-innovation stochastic gradient algorithm is derived by introducing the innovation length in the stochastic gradient algorithm. Then, the original system is transformed into two subsystems by using a filter. A filtering-based multi-innovation stochastic gradient algorithm is presented, whose parameter estimation accuracy is higher than the multi-innovation stochastic gradient algorithm. The simulation results confirm that these two algorithms are effective.

In this study, a novel global fixed-time synchronisation of uncertain complex dynamical networks including nonidentical nodes in the presence of unknown disturbances under input non-linearity constraint is investigated. First, in order to achieve the fixed-time synchronisation of network with unknown disturbances, a novel sliding manifold is established. The fixed-time stability of both the reaching and sliding modes are proved based upon the Lyapunov stability theorem. The notable feature of the proposed control is that the fixed convergence time of both reaching and sliding modes can be tuned to the desired values by selecting the designable parameters in advance. Finally, five numerical experiments are presented to demonstrate the validity of the obtained results as well as the practicability of the proposed methods.

This study presents a fault tolerant control (FTC) scheme based on fault estimation (FE) for a system subject to input saturation, uncertainty, -bounded disturbance and additive faults. In this study, the saturation is represented in polytopic form, and the disturbance is partitioned into matched and unmatched parts. For the FE scheme, a partially-decoupled unknown input observer is introduced to completely compensate for the matched part and only the unmatched part affects the FE performance. The FE and FTC schemes are integrated to ensure that the resulting closed-loop system is stable with -gain performance. Furthermore, all sufficient conditions for robust performance are derived and cast as linear matrix inequalities (LMIs). Usage of the Young relation removes equality constraints, and thus all LMIs are solvable in a single step. Numerical simulations are provided to verify the effectiveness of the proposed scheme.

This work strives for the issue of generalised dissipative asynchronous output feedback control for Markov jump repeated scalar non-linear systems with time-varying delay. The objective is to design an asynchronous output feedback controller, which ensures that the closed-loop system is generalised stochastically dissipative. Meanwhile, such an asynchronous controller covers not only the asynchronous controller but also the mode-independent one. By means of a stochastic analysis technique and a modified matrix decoupling method, sufficient conditions are given for deriving the desired controller. At length, an illustrative example is provided to demonstrate the availability of the presented approach.

This study is concerned with the output feedback stabilisation problem for a class of large-scale non-linear time-delay systems with unknown measurement sensitivities. The non-linear terms are assumed to be bounded by states or delayed states multiplied by outputs polynomial functions. The state observers are given by the dynamic gain control design technique. By constructing an appropriate Lyapunov–Krasovskii functional, the global asymptotic stability of the closed-loop control system is analysed. A numerical example is given to illustrate the effectiveness of the proposed control scheme.

In this study, the problem of output feedback sliding mode control of linear sampled-data multi-input–multi-output systems is considered. Existing sliding mode control schemes can attenuate the influence of an external disturbance by driving system states onto a sliding surface. However, they can exhibit high gains during transients, which can be where T is the sampling time period. To address this problem, a new strategy, which employs disturbance approximation, is proposed so that the control effort will be . The new method avoids deadbeat phenomena and hence, it will be less sensitive to noise. Theoretical analysis is provided to show the convergence and robustness of the proposed method. Simulations were conducted to show the efficiency of the proposed approach.

In this study, the stability problem of continuous-time switched systems composed fully of unstable subsystems is considered. Unlike the hybrid conditions derived in previous literature, this study used a novel time-dependent quadratic Lyapunov function approach and a convex sufficient condition for switched linear systems is proposed in the framework of bounded maximum average dwell time (BMADT). The resulting condition in this study is enforced using the sum of squares programming. Then, the condition for switched linear systems is extended to uncertain systems and the robust stability condition is derived. Moreover, a new stability result of continuous-time switched systems with all subsystems unstable is investigated based on the BMADT conditions. The simulation shows that it is better than the results in previous literature. Two numerical examples are proposed to illustrate the authors' approach.

Over the past few years, networked control systems (NCSs) have shown rapid progress and have indeed been very popular in terms of research as well as industrial applications. The issue of limited resources has been a fundamental problem in the translation of modern control techniques to NCS design. In order to address the aforesaid design challenge, an improved event-triggered adaptive backstepping control scheme is presented in this study for a class of uncertain NCSs with non-Lipschitz non-linearities under limited resources. Rather than a preselected constant threshold assumption, a well-designed and systematic triggering rule is derived based on the Lyapunov approach in order to satisfy bandwidth limitation and ensure system stability with acceptable transient performance. Relative to existing strategies in the literature, the proposed method leads to a substantially reduced number of transmissions with longer inter-event time. Thereby, the proposed algorithm exhibits more efficiency in resource utilisation. Simulation results on a networked control based robotic manipulator system illustrate the efficacy of the proposed adaptive scheme compared to benchmark control algorithms intended for a similar application.