Mourad Kchaou

Observer based (Q,V,R)-α-dissipative control for TS fuzzy descriptor systems with time delay

Abstract This paper is concerned with the design of ( Q , V , R ) - α - dissipative control for continuous TS fuzzy descriptor systems with unmeasurable states and time-varying delay. Our attention is focused on the design of the fuzzy controller and the fuzzy observer such that the closed loop fuzzy descriptor system with time delay is not only regular, impulse-free and stable but also ( Q , V , R ) - α - dissipative . By using the matrix decoupling technique, new delay dependent stabilization conditions are presented in terms of Linear Matrix Inequalities (LMI). As a particular case, observer-based H ∞ control is deduced from the proposed observer-based dissipative control result. Finally, a numerical example is given to demonstrate the effectiveness of our results.

Non-fragile H∞ output feedback control design for continuous-time fuzzy systems

In this paper, we investigate the problem of non-fragile H∞ fuzzy control design for continuous Takagi Sugeno (T-S) fuzzy systems with uncertainties, external disturbance and unmeasurable state variables. For the case of controller and observer gain additive variations, we propose a new solution of the fragility problem by developing the non-fragile design schemes ensuring the asymptotic stability and H∞ performance for the resulting closed loop systems. By considering a fuzzy Lyapunov function and by introducing slack variables, we propose the new sufficient stabilization conditions formulated in LMI constraints which can be easily solved using the convex optimization tools. The effectiveness the proposed results are illustrated through three numerical examples.

A new approach to non-fragile H ∞ observer-based control for discrete-time fuzzy systems

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.

Robust H∞ reliable control of time delay nonlinear systems via Takagi–Sugeno fuzzy models

This article is focused on reliable fuzzy H ∞ controller design for a class of Takagi–Sugeno (T–S) fuzzy systems with state delay, actuator failures, disturbance input and norm bounded uncertainties. In the design, the H ∞ performance of the closed-loop system is optimised during normal operation (without failures) while the system satisfies a prescribed H ∞ performance level in the case of actuator failures. Two methods are presented in this study. In the first method, delay-dependent conditions are derived based on a single Lyapunov–Krasovskii function. This method improves delay-independent results existing in the literature. Next, to further reduce the conservatism, we use a parameter-dependent Lyapunov–Krasovskii function. The new sufficient conditions for the existence of the suboptimal robust reliable controller are shown in terms of linear matrix inequalities (LMIs), which can be solved by using LMI optimisation techniques. A simulation example shows the effectiveness of the proposed methods.

DELAY-DEPENDENT H∞ RESILIENT OUTPUT FUZZY CONTROL FOR NONLINEAR DISCRETE-TIME SYSTEMS WITH TIME-DELAY

This paper is concerned with the problem of non-fragile (resilient) H∞ control for a class of state-delay nonlinear discrete-time systems described by (TS) fuzzy models where both the state feedback and static output feedback are investigated. Based on basis-dependent Lyapunov-krasovskii function, sufficient conditions are derived to achieve the system stability and the H∞ performance. The linear matrix inequality (LMI) approach is proposed to obtain the state-feedback gains, and a homotopy-based iterative LMI algorithm is developed to get the static output feedback gains. An illustrative example shows the effectiveness and the feasibility of the theoretical developments.

Robust reliable guaranteed cost piecewise fuzzy control for discrete-time nonlinear systems with time-varying delay and actuator failures

In this paper, we investigate the delay-dependent robust reliable guaranteed cost (RRGC) fuzzy control problem for discrete-time nonlinear systems with time-varying delays. The delays may simultaneously appear in the state and in the control input. Also, both parametric uncertainties and control component failure may exist. Through Takagi–Sugeno fuzzy modelling of nonlinear delayed-systems and based on an appropriate piecewise Lyapunov-Krasovskii functional, a piecewise fuzzy controller is designed. Sufficient conditions for the existence of a RRGC controller are derived in terms of linear matrix inequalities (LMIs). Furthermore, a suboptimal RRGC fuzzy controller is given by means of a convex optimization procedure with LMI constraints which can not only guarantee the stability of the closed-loop fuzzy system, but also provides an optimized upper bound of the given cost performance despite possible actuator faults. Two numerical examples are presented in this paper to illustrate the feasibility of the theoretical developments.

Control of Time Delay Fuzzy Descriptor Systems with Actuator Saturation

This paper investigates the stabilization problem of time delay fuzzy descriptor system under actuator saturation. A polytopic approach is used to describe the saturation behavior. By using an augmented Lyapunov–Krasovskii functional and adopting the delay partitioning technique, less conservative sufficient conditions are established to ensure the closed-loop system to be locally robust admissible. Moreover, a domain of attraction in which the admissible initial states are ensured to converge asymptotically to the origin is determined. In this paper, all the conditions are transformed into minimization problem involving LMI conditions by adopting the idea of the cone complementarity algorithm. This minimization problem can be solved efficiently by using the LMI optimization techniques. A numerical example illustrates the effectiveness of the design.

Robust stabilization conditions for time-delay fuzzy systems using fuzzy weighting-dependent approach

This paper investigates the problem of robust control design for a class of uncertain nonlinear systems with delay. The system is described by a state-space Takagi-Sugeno fuzzy model and norm-bounded parameter uncertainties. By evaluating the derivative of a new fuzzy weighting-dependent Lyapunov-Krasovskii functional, less conservative convex conditions, expressed as linear matrix inequalities (LMIs), are established. Two numerical examples are provided to show that our method can lead to much less conservative results than those in the existing references.

Resilient H∞ sliding mode control for discrete-time descriptor fuzzy systems with multiple time delays

ABSTRACT 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 the H∞ 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.

Robust H ∞ reliable networked static output feedback control design for vehicle dynamics stability

This paper investigates the problem of robust reliable static output feedback (RRSOF) controller design of vehicle lateral dynamic under unreliable communication link. The packet dropouts and network-induced delays, which are two typical network constraints of data transmission through network are considered. Also, both parametric uncertainties and control component failure may exist. Moreover, the disturbance attenuation is performed using a H∞ criterion. On the basis of a delay-dependent Lyapunov-Krasovskii functional, sufficient conditions for the existence of a RRSOF controller for asymptotic stability of resulting closed-loop networked control systems (NCS) are derived in terms of linear matrix inequalities (LMIs). Simulation results of the control performance shows the effectiveness of the proposed solution in terms of reliability and robustness.