This study addresses the asymptotic tracking problem subjected to linear quadratic (LQ) constraints for linear discrete-time systems, where packet dropout occurs in actuating channels. To solve this objective control problem, the controller-coding co-design approach is adopted, i.e. the controller, encoder and decoder are designed for taking full advantage of the network resource collaboratively, thereby achieving better transmission of control signals. A stabilisability condition in the mean square sense that reveals the fundamental limitation among the norm of the plant, data arrival rates and coding matrices is first derived. Then, a solvability condition is conducted to handle the additional stochastic LQ control objective by a modified discrete-time algebraic Riccati equation, and an iterative algorithm is also given for designing the corresponding state feedback gain and coding matrices. Relied on such design, the asymptotic tracking constraint is further fulfilled through solving a Sylvester equation, and the feedforward gain related to tracking is parameterised. Finally, a simulation with the implementation of the design method on two cooperative robots is included to show the effectiveness of the current results.

This study deals with the problem of state bounding for positive singular discrete-time systems with time-varying delay and bounded disturbances. First, the authors derive some new conditions for the existence of componentwise bounds of the state vector of the systems without disturbances. Then, in the case of systems with bounded disturbances, they obtain a sufficient condition for the existence of componentwise ultimate bounds. Since the conditions are given in terms of the spectral radius of the system matrices, they can check them easily and compute directly the smallest componentwise ultimate bound. In addition, the problem of state bounding for positive time-varying singular systems is also investigated in this study. Finally, numerical examples are provided to illustrate the effectiveness and advantages of their results.

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.

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.

The present study mainly focuses on designing a stochastic sampled-data controller for chaotic Takagi–Sugeno (T–S) fuzzy systems. Distinct to the existing controller schemes, in this work, the random time delay is introduced into the proposed control scheme that ensures the exponential stabilisation of T–S fuzzy models. In addition, the input delays are assumed to be randomly time-varying, which copes with the traditional uncorrelated Bernoulli distributed sequences. Based on the proposed Lyapunov–Krasovskii functional and using new weighted integral inequalities, the stability and stabilisation conditions are derived and expressed in terms of linear matrix inequalities, which ensure the exponential stability of the states. Finally, in the simulation results, the chaotic nature of two dynamical systems are considered for validation of the derived conditions. From the simulation results, it is concluded that the proposed method can provide better stability performance and less conservative results.

This study addresses the consensus problem for linear multi-agent systems subject to external disturbances under the leaderless framework. A novel distributed dynamic output feedback control protocol is proposed, which utilises not only relative output information of neighbouring agents but also relative state information of neighbouring controllers. Through model transformation, the consensus control problem of multi-agents network is reduced to a set of independent stabilisation subproblems for n-dimensional linear systems. Sufficient analysis conditions are derived using the Lyapunov method. An important contribution of this work lies in that the leaderless output-feedback consensus synthesis conditions are convexified without introducing any conservatism and formulated as linear matrix inequalities, which can be solved efficiently via convex optimisation. This is achieved by using a novel dynamic output-feedback controller structure. A numerical example has been used to demonstrate the advantage of theoretical results.

This study is concerned with dwell time stability and stabilisation problems of switched positive linear systems (SPLSs). The dwell time refers to minimum dwell time and constant dwell time. Several stability conditions for primal and transpose SPLSs with dwell time are presented, and the relation between these conditions is illustrated. Some of these conditions are given in terms of infinite-dimensional linear programming (LP), which cannot be solved directly. Then, by utilising the piecewise linear approach, new alternative convex conditions are formulated in terms of finite-dimensional LP. Compared to the existing literature, results with lower or at least the same conservatism can be obtained under the new conditions for the same discretised order. An algorithm is given to reduce the computational cost. Meanwhile, it is proved that there exists a relation between these convex and non-convex conditions if the discretised order is sufficiently large. By utilising the transpose conditions, alternative convex conditions on stabilisation of SPLSs with dwell time are also presented. The controller gain matrices can be computed by solving a set of LP directly. Finally, the correctness and superiority of the results are verified by numerical examples.

This study is concerned with the problem of designing a robust model predictive control (MPC) for a class of uncertain discrete-time Markov jump linear systems. The main contribution is a set of linear matrix inequality (LMI) conditions obtained under new control policies for the unconstrained as well as the constrained MPC when uncertainties are present both in the system's matrices and in the transition probabilities of the modes. For the constrained MPC, hard constraints are considered over the input control and the states and results are extended to the so-called multi-step mode-dependent state-feedback control design. To illustrate the improvements obtained with the new set of LMI conditions, numerical simulations are carried out and compared with a recent reference in the literature.

Sensor fault detection of discrete-time descriptor systems with bounded disturbances is studied. The authors propose a new structure of a fault detection observer by augmenting the output, which can broaden the application scope. A criterion is used to achieve the fault sensitivity and disturbance attenuation ability of the residual simultaneously. The residual generation and time-varying threshold calculation are integrated together based on analysis. Furthermore, sufficient conditions for the performance of the proposed observer are formulated in terms of linear matrix inequalities. Numerical simulations of a direct current motor and a flight vehicle are conducted to verify the applicability of the proposed fault detection observer design method.

In this study, an integrated fault tolerant preview tracking control framework is proposed based on reduced-order simultaneous state and fault estimation, robust preview control and fault signal compensation. In general, this work consists of three key design parts. Firstly, the analysis and synthesis conditions of a novel reduced-order simultaneous state and fault estimator are given based on the equivalent model reconstruction and optimisation of the parametric solution. Note that such a reduced-order design method can avoid traditional output equation reduction requirement, and has a wider application scope. Secondly, the robust preview tracking control policy is constructed by integrating state-feedback, preview action, and integral operation. Relying on augmentation modelling technique, a linear quadratic preview control design problem is transformed into an equivalent augmented state-feedback control design problem. Thirdly, the fault compensation is achieved by using estimated fault to accommodate fault influence. These involved designs are performed at the optimisation level, and thus guarantee the robust tracking performance of closed-loop systems. The effectiveness of the above conclusions is finally verified via two case studies.