Résumé: This article proposes a method for designing robust controller laws for a class of uncertain nonlinear parameter varying (NLPV) descriptor systems under input saturation and external disturbances. Both static and dynamic output feedback controllers are proposed. To synthesize the fuzzy controllers, the stability conditions are derived using polytopic parameter-dependent (PD) nonquadratic Lyapunov functions with respect to the given saturation constraint on the control input. First, the designed conditions are established in terms of linear matrix inequalities (LMIs) and gain performance is used to attenuate the effect of the external disturbance signals. Then, the estimation of the largest domain of attraction (DoA) for the system is formulated and solved as an optimization problem. Two examples are used to illustrate the effectiveness of the proposed design methods.

Résumé: This paper presents a new systematic controller design approach for disturbed nonlinear time-varying systems subject to input and state constraints in discrete-time case. The Takagi–Sugeno (TS) formalism and fuzzy Lyapunov framework are used to handle the time varying parameters and control input saturation. Moreover, the proposed control method is based on L 2 criterion which results in two different control design procedures. Both non-parallel distributed compensation (non-PDC) static state feedback control law and dynamics output feedback controller are proposed. To ensures the closed-loop system stability with respect to the given saturation constraints on the control input different optimization problem are also formulated in terms of linear matrix inequality conditions which can be solved efficiently with available solvers. The proposed techniques are illustrated through numerical examples.