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.

Résumé: Precise control of overhead crane systems with input saturation , especially when there are disturbances is essential to ensure both operational safety and efficiency. This paper focuses on the control of overhead cranes with variable cable lengths, employing the Takagi-Sugeno (T-S) fuzzy modeling approach. By decomposing the nonlinear dynamics into a set of local linear sub-models corresponding to different operating regions, the T-S fuzzy method enables effective handling of the system’s inherent nonlinearities. To further improve performance under input saturation, a non-Parallel Distributed Compensation (non-PDC) controller is integrated into the control design framework. Using Lyapunov theory, the controller synthesis is formulated using linear matrix inequalities (LMIs), which are solved to determine the controller parameters. Robust performance is achieved by incorporating H∞ or L∞ performance criteria into the fuzzy control model, ensuring disturbance rejection. Finally, simulation results are presented to validate the effectiveness and performance of the proposed control strategies.

Résumé: This paper treats the stabilization analysis for a class of nonlinear descriptor systems subject to input saturation and unknown disturbance. The synthesized control strategy is based on the Takagi-Sugeno design approach and a non-parallel distributed compensation (non-PDC) control law. Stabilization conditions are derived using non-quadratic Lyapunov functions to ensure the closed-loop system stability despite the given saturation constraint on the control input. The optimization problem is formulated in terms of linear matrix inequalities (LMIs). The technique is illustrated through numerical examples.