Mansour Souissi

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.

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

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

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

H_\infty

Observer design for fault diagnosis for the Takagi-Sugeno model with unmeasurable premise variables

H∞ approach. In order to obtain both the observer and the controller gains the design conditions are formulated in Linear matrix inequality terms which can be solved using a one-step design procedure. Finally, the FTTC strategy is illustrated on a two-tank system to show its effectiveness.

Fuzzy Tracking Control for Indirect Field-oriented Induction Machine Using Integral Action Performance

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 flux and load torque estimation in Induction Machine

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.

Improvement on observer-based H ∞ tracking control for TS fuzzy systems with unmeasurable premise variables

In this paper, a robust fuzzy observer-based tracking controller for continuous-time nonlinear systems presented by Takagi–Sugeno (TS) models with unmeasurable premise variables, is synthesized. Using the H∞ norm and Lyapunov approach, the control design for TS fuzzy systems with both unmeasurable premises and system states is developed to guarantee tracking performance of closed loop systems. Sufficient relaxed conditions for synthesis of the fuzzy observer and the fuzzy control are driven in terms of linear matrix inequalities (LMIs) constraints. The proposed method allows simplifying the design procedure and gives the observer and controller gains in only one step. Numerical simulation on a two tank system is provided to illustrate the tracking control design procedure and to confirm the efficiency of the proposed method.

Robust Sensor Fault-Tolerant Control of Induction Motor Drive

This paper deals with the problem of the state estimation and the sensor faults detection for discrete time nonlinear systems described by Takagi-Sugeno (TS) fuzzy models with unmeasurable premise variables. Indeed, a TS observer is synthesized, in descriptor form, to estimate both the system states and the sensor faults simultaneously. The idea of the proposed approach is to introduce the sensor fault as an auxiliary variable in the state vector. Besides, the multiple model with unmeasurable premise variables is reduced to a perturbed model with measurable variables. Convergence conditions are established with Lyapunov theory and the L2 optimization in order to guarantee the convergence of the state estimation error. These conditions are expressed in terms of Linear Matrix Inequalities (LMIs). The gains matrices of the multi-observers are characterized using the solution existence of the LMI conditions. Finally, the model of an hydraulic system with three tanks is used to validate the proposed approach.