Hamdi Gassara

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.

Control of Time Delay Polynomial Fuzzy Model Subject to Actuator Saturation

This article is concerned with the design of polynomial fuzzy controller for a class of polynomial fuzzy model subject to both state delay and actuator saturation. Based on polytopic model of the input saturation, two design methods are proposed. In the first method, a specific Lyapunov Krasovskii function is proposed to transform the nonconvex sum of squares (SOS) conditions into convex SOS ones. The second method overcomes the restriction of the first method by bounding the state derivative. The obtained results are formulated in terms of SOS matrices which can be symbolically and numerically solved via the SOSTOOLS and the SeDuMi. Moreover, an attractive region of initial states that ensures asymptotic stability of polynomial fuzzy model is determined. Two numerical examples are given to show the effectiveness of the proposed methods.

Design of polynomial fuzzy observer–controller for nonlinear systems with state delay: sum of squares approach

ABSTRACT This paper investigates the problem of observer-based control for two classes of polynomial fuzzy systems with time-varying delay. The first class concerns a special case where the polynomial matrices do not depend on the estimated state variables. The second one is the general case where the polynomial matrices could depend on unmeasurable system states that will be estimated. For the last case, two design procedures are proposed. The first one gives the polynomial fuzzy controller and observer gains in two steps. In the second procedure, the designed gains are obtained using a single-step approach to overcome the drawback of a two-step procedure. The obtained conditions are presented in terms of sum of squares (SOS) which can be solved via the SOSTOOLS and a semi-definite program solver. Illustrative examples show the validity and applicability of the proposed results.

Observer based dissipative reliable control for Takagi-Sugeno fuzzy systems with time delay

This paper is concerned with the design of α-dissipative reliable control for continuous Takagi-Sugeno (T-S) fuzzy systems with unavailable states and time-varying delay. The sufficient conditions for the existence of fuzzy observer and the α-dissipative reliable fuzzy controller are given in terms of Linear Matrix Inequalities (LMI) which can be solved efficiently by using the LMI optimization techniques. The conditions are obtained by using a free weighting matrix technique (Newton Leibniz formula) without imposing model transformation which reduce the conservatism. The obtained LMI are dependent, not only upon upper bound of time delay, but also on the dissipative margin α and on the actuator failure parameter. Furthermore, a more general actuator failure model is adopted in this paper, which covers the typical work status of actuator, i.e. normal operation, partial degradation and outage. The results of H∞ performance, positive realness and mixed of H∞ and positive real performance are easy corollaries of the dissipative result. A numerical example is given in order to demonstrate the effectiveness of our result.

New Polynomial Lyapunov Functional Approach to Observer-Based Control for Polynomial Fuzzy Systems with Time Delay

This paper presents a new Line-integral polynomial Lyapunov functional approach for observer-based control for a class of polynomial fuzzy systems with time delay and unmeasured state variables. To guarantee the global asymptotic stability and estimation error convergence, a design method is proposed. In this work we consider a Line-integral polynomial Lyapunov function in which the Lyapunov matrices are polynomial matrices depending not only of the estimated states but also of the estimated delayed states and we use the dual system to reduce the computational efforts. The design conditions are established in terms of Sum Of Squares (SOS) which can be numerically and symbolically solved via the recent developed SOSTOOLS and a Semi-Definite Program solver. Finally, numerical examples are proposed to show the validity and applicability of the proposed results .

Stability conditions for time delayed Takagi-Sugeno systems

This paper deals with stability of time delayed Takagi-Sugeno (TS) fuzzy systems. By considering a linear function which bound the derivative of fuzzy weighting functions, a relaxed stability method is established. A new stability approach is derived for time delayed TS systems by using integral Lyapunov function. To show the advantages of the proposed approaches, an illustrative example is given.

New approach of stability analysis for polynomial fuzzy model with time delay

The actual paper study a new approach of stability analysis for polynomial fuzzy model (PFM) with delay time. We introduced a polynomial Lyapunov-Krasovskii function to explore the system stability. A new approach is procured to get a feasible solution, which can be solved via SOSTOOLS. Finally, the less conservativeness of the present result is illustrated by numerical examples.