This study focuses on the asymptotic stability and stabilisation of uncertain linear systems with time-varying delays via delta operator approach. By employing a new model formulation, the time-delayed delta operator system is transformed into an interconnected system for which the uncertainties can become easy to deal with. Based on a two-term approximation of delayed state and scaled small gain theorem, new delay-dependent sufficient conditions of robust asymptotic stability and state-feedback stabilisation of an uncertain delta operator time-delayed system are established by using a novel Lyapunov–Krasovskii functional. The criteria obtained unify some previously suggested relevant methods seen in literature for achieving asymptotic stability and stabilisation of both continuous and discrete systems into the delta operator framework. Numerical examples presented explicitly demonstrate the advantages and effectiveness of the proposed methods.

In this study, a distributed model reference adaptive control architecture is developed to achieve the cooperative tracking of uncertain dynamical multi-agent systems, where the reference model serves as a virtual leader for the group to track. Two adaptive laws, with one adjusting the coupling weights and the other adjusting the neural network weights, are designed based on the relative state information of neighbouring agents. The proposed controller guarantees that the state of each agent synchronizes to that of the reference model over any undirected connected communication graphs, and all signals in the closed-loop network are uniformly ultimately bounded. In contrast to the existing results, the developed controller can be implemented in a fully distributed manner by each agent without using any global information and the accurate model of each agent. An extension to asymptotic stability is further studied.

This study investigates systems where the sensors and the actuators are driven by two independent random events so that at any time only a subset of them is activated. The triggering events are modelled by two Markov chains with partially unknown transition rates. The authors derive a systematic control analysis and synthesis framework using theories in Markovian jumping systems and time-delay systems. The results are given in terms of the delay bounds and the transition probabilities of the Markov chains, which are obtained by using a newly defined Lyapunov–Krasovskii functional and the weak infinitesimal operator. A numerical example is given to demonstrate the effectiveness of the proposed method.

This study discusses the problem of decentralised output-feedback control for a class of stochastic non-linear systems under weaker conditions. Based on the adding one power integrator technique and homogeneous domination approach, a homogeneous observer and controller are constructed for each nominal subsystem without the perturbing non-linearities. Then, a scaling gain is introduced into the homogeneous observers and controllers to render the closed-loop system to be globally asymptotically stable in probability. Two simulation examples are provided to show the effectiveness of the control scheme.

In this work, an adaptive vector controller is designed for a three-phase voltage source converter (VSC) to provide power factor compensation. The method relies on a third-order non-linear model of the VSC, which includes parametric uncertainty. The proposed method ensures asymptotic tracking of the q-axis current using an inner loop, which contain two proportional–integral (PI) controllers that have adaptive decoupling terms. The output of an outer loop PI controller for dc voltage defines the reference for the d-axis current control. The asymptotic stability of the closed-loop is proven using Lyapunov's method. The performance of the proposed method is evaluated in simulation and experiment, and results show improved performance and ease of controller tuning.

This study is concerned with the fault detection (FD) problem for a switched linear parameter-varying system, which is modelled by some different operating points of flight envelope. FD filters are designed such that the estimation errors between the residual signals and the faults are minimised for disturbances, faults and time-varying parameters. By the aid of the parameter-dependent multiple Lyapunov functions method, sufficient conditions for the solvability of this problem are formulated by linear matrix inequalities, furthermore, the filter gains are characterised in terms of a convex optimisation problem. A simulation on the longitudinal motion of Highly Maneuverable Aircraft Technology vehicle is given to demonstrate the effectiveness of the proposed methods.

Traditional maximally permissive deadlock prevention control for flexible manufacturing systems requires costly reachability analysis. It has been a hot race to synthesise optimal controllers to be maximally permissive with fewest monitors. Previous work shows that among all n-dependent siphons, only one siphon (whose unmarked state follows some token distribution) needs to be controlled. This greatly simplifies the supervisor synthesis as well as minimises the number of monitors required while making the controlled net maximally permissive (i.e. all live states can be reached.). This study further proposes a maximally permissive control policy for a subclass of systems of simple sequential processes with resources (S³PR) based on the above theory of token distribution pattern of unmarked siphons.

This study addresses reduced-order dynamic observer error linearisation (RDOEL) for discrete-time systems, which is a modified version of dynamic observer error linearisation (DOEL). The authors define the concept of RDOEL and provide a necessary and sufficient condition for RDOEL. Moreover, the relation between RDOEL and DOEL is discussed when the auxiliary dynamics is an arbitrary linear controllable system. Using the relationship and an existing algorithm for DOEL, an algorithm for RDOEL also proposed, which offers lower-dimensional observers than DOEL. Finally, the authors illustrate the theory by applying it to the discrete-time hyperchaotic system due to Wang, which was derived from the generalised Rössler system via a first-order difference algorithm.

Since quantum system, which is one of the foci of ongoing research, is the classical example of complex-valued systems, in this study, the stability of complex-valued impulsive system is addressed. Taking advantage of the Lyapunov function in the complex fields, the stability criteria of complex-valued impulsive system are established, which not only generalises the stability criteria on real-valued impulsive system, but also greatly reduces the complexity of analysis and computation. Moreover, as an application, a linear impulsive feedback controller for the complex-valued Lü system is designed.

An iterative linear matrix inequality (LMI) approach is proposed to design fault-detection filters (FDFs) of uncertain linear time-invariant (LTI) systems. The obtained FDF is the optimal solution for the H _i /H _∞ (with H _∞/H _∞ and H ₋/H _∞ being two extreme cases) optimisation problem of FDF design and can achieve the best trade-off between robustness against unknown disturbances and sensitivity to system faults. The authors first derive the theoretical optimal H _i /H _∞ FDFs for uncertain LTI systems based on the co-inner–outer factorisation technique. Then a new optimisation problem is formulated to obtain the optimal FDFs that can approach the theoretical optimal ones as much as possible. An iterative LMI approach is presented to find the solution in the state-space form. The effectiveness of the proposed approach is illustrated by a numerical example.

Consensus problems for first-order continuous-time swarm systems in directed networks with time delays and topology uncertainties are dealt with. The state space of a swarm system is decomposed into a null space and a complement null space. By projecting the state of the system onto the two subspaces, a necessary and sufficient condition for consensus is proposed, and an explicit expression of the consensus function is shown based on the impacts of time delays and topology uncertainties. Sufficient conditions in terms of linear matrix inequalities are given for swarm systems with time-varying delays and topology uncertainties to achieve consensus. Numerical examples are shown to demonstrate theoretical results.

This study addresses the input-to-state stability (ISS) of non-linear impulsive and switched delay systems. Based on the piecewise Lyapunov–Krasovskii functional method, the authors show that when only some of the constituent subsystems are ISS, the ISS property still can be retained for the non-linear impulsive and switched delay system, if the dwell time of the ISS subsystems satisfies a lower bound condition and the activation time of the non-ISS subsystems satisfies an upper bound condition, respectively. In common parlance, some of the intervals must be overly long, whereas the others must be short enough between impulses. Compared with existing results on related problems, the theory can be applied to a larger class of systems. The proposed approach also enables us to give the analysis of systems involving actuator failure, controller failure or temporary uncertain switching signal. As an example, the authors employ the method to analyse the problem of reliable control for a mechanical rotational cutting process.