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In this paper, the problem of asynchronous sliding mode control (SMC) is addressed for discrete-time singular Markovian jump systems (DSMJSs) with external disturbances and randomly occurring nonlinearities. Moreover, the states of DSMJSs are unavailable for measurement, and the synchronisation between the controller and the system modes is not surely ensured. Our attention is mainly focused on solving the control problem by proposing an observer-based adaptive sliding mode controller for such a class of complex systems. First, a non-fragile observer is designed not only to estimate the system states but also to relax the multiplicative gain variations and to construct an appropriate mode-dependent sliding mode surface function. Then, by assuming that the bounds of nonlinear terms are unknown, an adaptive SMC control law is synthesised to drive the system trajectories onto the specified sliding surface and completely compensate for the influences of the external disturbances and fluctuations of the controller and observer gains. Sufficient conditions are established to ensure that the closed-loop system is stochastically admissible with a γ level of the mixed H ∞ /passive performance, and to provide the observer and controller gain matrices. Finally, to numerically substantiate the efficacy of the proposed control scheme, two examples are given. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of -admissibility analysis and synthesis for a class of uncertain continuous fuzzy descriptor systems. By adopting the linear matrix inequality approach and introducing some free matrices, sufficient conditions are established to ensure the -admissibility of the considered class of nonlinear uncertain descriptor systems. From this formulated criterion, a static output feedback multi-controller is designed to ensure the admissibility of the closed loop fuzzy descriptor systems and to improve the transient performances in a union of sub-regions. The merit and effectiveness of the proposed conditions are illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]

In this study, a decentralised output learning control strategy for a class of nonlinear interconnected systems is studied. Based on Takagi-Sugeno fuzzy (TS) model to approximate the considered interconnected nonlinear systems, a decentralised observer-based control scheme is designed to override the external disturbances such that theperformance is achieved. The appealing attributes of this approach include: (1) the closed-loop system exhibits a robustness against nonlinear interconnections and external disturbance, (2) by one-step procedure, the gain matrices of observer and controller are obtained on a single step. In simulation results, the controller design is evaluated on the steering stability of a car where the nonlinear model describes the side slip, roll and yaw motions of the automotive vehicle equipped with four-wheel-steering and active suspension. [ABSTRACT FROM PUBLISHER]

The resilient sliding mode control (SMC) problem for a class of discrete-time descriptor Takagi–Sugeno (T-S) fuzzy systems with multiple state delays is addressed. Attention is focused on the design of a discrete-time SMC such that the admissibility as well as theH∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delays and external disturbances. Based on a new sliding function, a delay-dependent sufficient condition is established to ensure the desired performance of the sliding mode dynamics on the specified sliding mode surface. Moreover, a resilient SMC law is established to satisfy the reaching condition. Finally, two examples are given to show the effectiveness and advantages of the proposed design SMC scheme. [ABSTRACT FROM AUTHOR]

In this article, a new approach regarding H ∞ and non-fragile stability analysis and observer-based controller synthesis problem for a class of discrete-time fuzzy systems is investigated. The multiplicative gain variations under consideration are contained in both the controller gain and observer gain. By defining a basis-dependent Lyapunov function and introducing some additional matrix variables, new sufficient conditions are derived to guarantee the stability of the non-fragile H ∞ observer-based control system. Seeking computational convenience, the developed results are cast in the format of linear matrix inequalities and two numerical examples are presented to illustrate the feasibility of theoretical developments. [ABSTRACT FROM AUTHOR]