This study focuses on the problem of stability analysis and stabilisation for discrete time-delay systems. A new type of augmented Lyapunov–Krasovskii functional (LKF) is proposed to derive less conservative stability and stabilisation conditions. A novel inequality is developed to handle more general double summation terms which arise from the forward difference of augmented LKF. Several zero equalities are introduced to further relax the existing results. Using some advanced convexificator techniques, the derived stability and stabilisation conditions are presented in terms of linear matrix inequalities. Several numerical examples are provided to demonstrate the advantage of the proposed approach.

In this study, finite-time passivity of switched non-linear systems is developed. First, a finite-time passivity concept is proposed using multiple storage functions. Second, a switching law is designed to make a switched non-linear system finite-time passive. Third, on the basis of the proposed concept, finite-time passivity properties are investigated. On the one hand, finite-time passivity can induce finite-time stability. On the other hand, finite-time passivity is preserved under the feedback interconnection and parallel interconnection. Furthermore, the merging switching signal technique is employed to make an interconnected system finite-time passive. Finally, an example is provided to demonstrate the effectiveness of the obtained results.

This paper employs the observer-based output feedback control technique to study the problem of local piecewise control for a linear parabolic partial differential equation(PDE) using non-collocated local piecewise observation. By the non-collocated local piecewise observation, a Luenberger-type PDE observer is first constructed to exponentially track the state of the PDE in the sense of both norm and norm. Based on the estimated state, a collocated local piecewise state feedback controller is then proposed for exponential stabilisation of the PDE. Sufficient conditions on exponential stabilisation of the PDE by the suggested feedback controller in the sense of both norm and norm are developed by utilising Lyapunov direct method, integration by parts, Wirtinger's inequality, and first mean value theorem for definite integrals, and presented in terms of standard linear matrix inequalities. The well-posedness is also analysed for both open-loop and resulting closed-loop PDE by using -semigroup approach. Finally, numerical simulation results are presented to show the effectiveness of the proposed design method.

This study concerns the stability analysis of linear large-scale fractional-order systems and its functional observers design. First, based on the diffusive representation of the fractional-order derivative and the indirect Lyapunov approach, the stability of large-scale fractional-order interconnected systems is studied. Then, a sufficient stability condition of such systems is given in linear matrix inequality (LMI) formulation. In the second part of this work, the existence conditions of functional decentralised observers for this class of systems are given, and the asymptotic stability of estimation errors is investigated. The observers gains matrices are derived by solving the obtained LMI. Numerical examples are given to illustrate the validity of the proposed approach.

The problem of robust fault detection (FD) filter design for interconnected systems, and the problems of both packet dropouts and disconnected interconnections in these subsystems are studied. By modelling instances of disconnected interconnections among subsystems and packet dropouts in the measurement channel into independent subsystems, this study proposes a switched scheme that combines mode-dependent average dwell time with event-driven switching. A filter in which the FD system is exponentially stable and achieves a weighted performance can be derived from the optimal method of convex linear matrix inequalities. An example is given to demonstrate the effectiveness of the proposed method.

This study presents an adaptive sliding mode synchronisation scheme for a class of fractional-order non-linear systems in the presence of unknown parameters, actuator faults, and disturbances. The designed adaptive controller compensates a general class of actuator faults without the need for any explicit fault detection. The parameters, times, and patterns of the considered faults are completely unknown. The proposed adaptive sliding mode synchronisation scheme can guarantee the asymptotic convergence of the synchronisation error to the origin despite the presence of actuator faults and uncertainties. The simulation results show the correctness and effectiveness of the proposed adaptive sliding mode fault compensation approach.

The objectives of this study are five-fold: (i) design an extended Kalman filter (EKF) for the single-muscle and two-muscle Hill models; (ii) design an EKF for unknown-input estimation of the muscle models; (iii) investigate the detectability of the muscle models; (iv) examine the robustness of the EKF to modeling errors; and (v) improve state estimation by incorporating physical constraints into the estimator. Two noisy measurements are available for state estimation: muscle length, which is measured from joint angles; and muscle activation, which is measured from electromyography sensors. Simulation results verify that the EKF is an effective approach for estimation of the activation signals and the states of the system if the system is detectable; the EKF outperforms the high gain observer; and the EKF is robust to modeling errors. The standard deviations of the estimation errors are in the range 0.01–0.1 mm for the muscle lengths, which is one to two orders of magnitude more accurate than the measurements. The standard deviations of the dimensionless muscle activation estimation errors are in the range 0.01–0.02, which is one order of magnitude more accurate than the measurements. A projection approach accounts for constraints to further improve the estimates.

In this study, the author studies fixed-time group consensus problem in networks of dynamic agents with intrinsic non-linear dynamics and bounded uncertainties. Three types of distributed control protocols are proposed to achieve fixed-time group consensus when the subgroups are connected and have inter-group common influence. By using Lyapunov theory, algebraic graph theory, and fixed-time stability, some conditions are derived to select the controller gains to ensure the convergence in a prescribed time regardless of the initial conditions. Numerical examples are worked out to illustrate the effectiveness of our theoretical results.

This study investigates the active fault tolerant control (FTC) problem for the attitude system of a rigid satellite, which is affected by parameter uncertainty, unknown exogenous disturbance and actuator time-varying faults. The upper bounds of the actuator time-varying fault and the generalised perturbation are unknown. A novel adaptive non-linear fault estimation observer is designed in order to obtain the estimated value of unknown time-varying faults. Then, an active fault tolerant attitude control approach is proposed under the framework of both backstepping control and adaptive control theory. Consequently, the Lyapunov theory is used to prove the robust asymptotic stability for the closed-loop attitude system of a faulty satellite under the proposed FTC scheme. Finally, simulation results on an in-orbit rigid satellite are provided to show the good fault tolerant performance, which validate the effectiveness and feasibility of the proposed scheme.

The convergence of a new closed-form solution for the discrete-time optimal control is presented. First, a new time optimal control law with simple structure is constructed in the form of the state feedback for a discrete-time double-integral system by using the state backstepping approach. The control signal sequence in this approach is determined by the linearised criterion according to the position of the initial state point on the phase plane. This closed-form non-linear state feedback control law clearly shows that time optimal control in discrete time is not necessarily the bang-bang control. Second, the convergence of the time optimal control law is proved by demonstrating the convergence path of the state point sequence driven by the corresponding control signal sequence. Finally, numerical simulation results demonstrate the effectiveness of this new discrete-time optimal control law.

This study is concerned with the problem of robust normalisation and stabilisation of singular Markovian jump systems (SMJSs) with time-varying delays and parameter uncertainties. The main aim is to design a proportional and derivative state feedback controller to realise the normalisation and stabilisation of the delayed SMJSs. Based on the constructed Lyapunov–Krasovskii functional, sufficient conditions are presented in terms of linear matrix inequalities via utilising the free-weighting matrix method. Illustrative examples including an resistor inductor capacitor (RLC) circuit network are employed to demonstrate the effectiveness and usefulness of the obtained results.

This shows that sufficient conditions of theorems in the above study cannot be derived by the proof method presented by the authors. The reason analysis is discussed in detail. Counterexamples are given to validate the conclusion.