N. Benhadj Braiek

Unknown Input Observer Design for Fuzzy Bilinear System: An LMI Approach

A new method to design a fuzzy bilinear observer (FBO) with unknown inputs is developed for a class of nonlinear systems. The nonlinear system is modeled as a fuzzy bilinear model (FBM). This kind of T-S fuzzy model is especially suitable for a nonlinear system with a bilinear term. The proposed fuzzy bilinear observer subject to unknown inputs is developed to ensure the asymptotic convergence of the error dynamic using the Lyapunov method. The proposed design conditions are given in linear matrix inequality (LMI) formulation. The paper studies also the problem of fault detection and isolation. An unknown input fuzzy bilinear fault diagnosis observer design is proposed. This work is given for both continuous and discrete cases of fuzzy bilinear models. Illustrative examples are chosen to provide the effectiveness of the given methodology.

On Feedback Control Techniques of Nonlinear Analytic Systems

This paper presents three approaches dealing with the feedback control of nonlinear analytic systems. The first one treats the optimal control resolution for a control-affine nonlinear system using the State Dependant Riccati Equation (SDRE) method. It aims to solve a nonlinear optimal control problem through a Riccati equation that depends on the state. The second approach treats a procedure of constructing an analytic expression of a nonlinear state feedback solution of an optimal regulation problem with the help of Kronecker tensor notations. The third one deals with the global asymptotic stabilization of the nonlinear polynomial systems. The designed state feedback control law stabilizes quadratically the studied systems. Our main contribution in this paper is to carry out a stability analysis for this kind of systems and to develop new sufficient conditions of stability. A numerical-simulation-based comparison of the three methods is finally performed.

Robust residual generator design for Takagi-Sugeno fuzzy bilinear system subject to unknown inputs

Abstract In this paper, a method to design a residual generator for Takagi-Sugeno fuzzy bilinear system subject to unknown inputs and unmeasurable disturbances is proposed. The aim of this approach is to detect and isolate actuator faults despite the presence of disturbances. Such residual generator is determined on the basis of Linear Matrix Inequalities (LMIs) conditions. An example illustrates the effectiveness of the designed residual generator with unknown inputs and unmeasurable disturbances.

Observer-based controller for nonlinear analytical systems

In this paper, we propose to design a polynomial observer-based control for nonlinear systems and to determine sufficient linear matrix inequality (LMI) global stabilisation conditions of the polynomial controlled system augmented by its observer. The design of the observer-based control leverages some notations from the Kronecker product and the power of matrices properties for the state space description of polynomial systems. The stability study of the polynomial controlled system augmented by its observer is based on the Lyapunov stability direct method. Intensive simulations are performed to illustrate the validity and the effectiveness of the polynomial approach used to design the control.

A polytopic proportional integral observer design for fault diagnosis

In this paper, the problem of actuators faults detection and estimation for linear parameters varying systems described by the polytopic representation is considered by the design of a Polytopic Proportional Integral Observer (PPIO). The PPIO gains are obtained by solving a set of linear matrices inequalities. The proposed approach is applied, with success, to a Van de Vusse reactor.

Polynomial observer design for unknown inputs polynomial fuzzy systems: A Sum of Squares approach

This paper deals with a polynomial fuzzy observer (PFO) design for a class of nonlinear continuous systems that can be modeled as polynomial fuzzy systems (PFS) subject to unknown inputs. The proposed polynomial observer is developed to ensure the asymptotic convergence of the observing error using the Lyapunov method and numerical tools. Sufficient design conditions are given in Sum Of Squares (SOS) formulation which can be numerically solved via the SOSTOOLS software and a semidefinite program (SDP) solver. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

Robust non-fragile control of a class of nonlinear uncertain systems

This paper proposes a method to design a stabilizing Robust non-fragile control of uncertain polynomial systems. Based on a quadratic Lyapunov Function, a sufficient stabilization conditions are proposed. An LMI-based optimization problem is then derived for computing the state feedback gains of the closed-loop system with maximization of the stability robustness bound. The effectiveness of the proposed robust control scheme is illustrated through numerical simulations on a numerical example.