Mohamed Chaabane

Observer-Based Robust

In this paper, a method of robust H∞ reliable control for uncertain Takagi-Sugeno (T-S) fuzzy systems with unavailable states and time-varying delay is developed. In terms of linear-matrix inequalities (LMIs), we derive sufficient conditions for the existence of the fuzzy observer and the reliable fuzzy controller. The single-step LMI conditions, depending on the size of the delay, are proposed for the observer-based H∞ reliable controller design. This overcomes the drawback of two-step LMI approach in literature. Moreover, the designed fuzzy controller is reliable in the sense that the stability and the satisfactory performance of the closed-loop system are achieved not only under normal operation but in the presence of some actuator faults as well. The result is given without the assumption of the rate of change of time-delay function (i.e., |τ̊| <; 1), which makes it applicable to both slow and fast time-varying delayed systems. Without considering reliability, the proposed result is much less conservative than most of the existing results. Finally, several examples are given to show the effectiveness and advantages of our results.

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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.

Reliable Control for Uncertain T–S Fuzzy Systems With State Time Delay

This paper deals with the problems of robust stability and stabilization for uncertain continuous descriptor systems. We propose a new necessary and sufficient condition in terms of a strict linear matrix inequality (LMI) for a nominal continuous descriptor system to be admissible (stable, regular, and impulse-free). Based on this, the state-feedback admissibility problem is solved and the solution is extended to the case of uncertain descriptor systems. Finally, numerical examples are given to illustrate the results.

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

This article focuses on the problem of robust H ∞ control for uncertain T–S fuzzy systems with time-varying delay. By employing a novel technique, new delay-dependent stabilisation conditions for the existence of a robust H ∞ controller are obtained based on the parallel distributed compensation method. The result obtained is an important contribution as it establishes a new way that can reduce the conservatism without imposing any restrictions and computational efforts at the same time. In this article, all the conditions are shown in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using LMI optimisation techniques. Two numerical examples are given to demonstrate the merits of the approach proposed in this article. Finally, application to control a truck-trailer is also given to demonstrate the effectiveness of the proposed design method.

Stability and stabilization of continuous descriptor systems: An LMI approach

This brief is concerned with the design of observer-based controllers for continuous-time positive linear systems with interval uncertainties and time delay. More precisely, the problem of positive stabilization by observer-based static state-feedback controllers is investigated, taking into account that the nonnegativity of the error signals and the positivity of the augmented system are necessary to guarantee the stability of the closed-loop system and keep it positive at the same time. The proposed design methodology, which is based on linear matrix inequality conditions, is also illustrated by an example.

Robust H∞ control for T-S fuzzy systems with time-varying delay

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.

Static State-Feedback Controller and Observer Design for Interval Positive Systems With Time Delay

This paper deals with the H∞ estimation of both system state and faults for T-S (Takagi-Sugeno) fuzzy model with bounded input disturbances. Based on the descriptor technique, the sensor faults are considered as an auxiliary state variable. Then a descriptor observer for the obtained augmented system is designed and the observer gains are determined in LMI (Linear Matrix Inequalities) formulation. This method has the advantage to estimate the state variables and the sensor faults simultaneously with H∞ approach. Numerical example shows the efficiency of the proposed method.

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

This paper discusses the problem of fault-tolerant tracking control (FTTC) for fuzzy nonlinear systems with unmeasurable premise variables. To simultaneously estimate the system states and the sensor faults, a fuzzy descriptor observer is developed. Then, a fault-tolerant controller to track the desired reference trajectories is synthesized. The sufficient stability conditions of the appropriate nonlinear augmented system are derived via the Lyapunov theory and the

Fault-Tolerant Trajectory Tracking Control for Takagi---Sugeno Systems with Unmeasurable Premise Variables: Descriptor Approach

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