Fuzzy controller design for nonlinear singular systems with external noises subject to passivity constraints

Abstract

This paper applies the state derivative feedback method and proportional plus derivative state feedback method to design the fuzzy controllers for the nonlinear singular systems with external noises. The Takagi‐Sugeno fuzzy modeling technology is employed in this paper to represent the nonlinear singular systems with external noise. Considering the singular Takagi‐Sugeno fuzzy model, the passivity constraint is chosen to treat the external noises for the controlled systems. By using the parallel distributed compensation method, the fuzzy controller is designed to satisfy the Lyapunov stability conditions and passivity constraints simultaneously. These sufficient conditions can be effectively solved in terms of linear matrix inequalities, which can be solved via the convex optimization technique. At last, some numerical examples are provided to verify the applicability and effectivity of the proposed fuzzy controller design methods.

Passive Decentralized Fuzzy Control for Takagi-Sugeno Fuzzy Model Based Large-Scale Descriptor Systems

“…Based on the inequalities (23)(24)(25)(26)(27), then one can rewrite the Lyapunov function (22) as follows:…”

“…Therefore, the stability analysis of the descriptor system is an important issue. In recent years, the stability analysis of the descriptor systems and T-S LSD systems have been discussed in [24][25][26][27].…”

Robust Decentralized Fuzzy Controller Design for Nonlinear Large-Scale Interconnected Descriptor Systems

“…Moreover, it should also be noted that the stability condition designed by the PD control method is often formulated as the bilinear matrix inequalities. By using Schur complement [19], the stability conditions are effectively recast into the LMI form. At last, a numerical example is provided to show the effectivity of the proposed robust decentralized fuzzy controller.…”

Observer-Based Fuzzy Controller Design for Nonlinear Discrete-Time Singular Systems via Proportional Derivative Feedback Scheme

“…However, if only using a traditional state feedback controller to singular systems, the complex model transformations for system matrices are unavoidable. To simplify the derivation process of the stability criteria, the PD feedback scheme was used to discuss control problems in [25][26][27][28][29][30][31][32]. For instance in [25] the stabilization issues for continuous-time and discretetime linear switched singular systems were studied via PD control strategy with the free-weighting matrix technique.…”

“…In [26], the passive H ∞ control for the discrete-time linear switched singular systems was studied by using the Schur lemma. The related PD control problems were studied in [27][28][29][30][31][32]. The PD observer issue for discrete-time singular systems was studied in [33].…”