Fuzzy Stabilization Approaches

Abstract

This chapter presents, in the first section, a generalized approach to state feedback stabilization of interconnected fuzzy systems. A convex optimization algorithm provides a decentralized solution to the problem of asymptotic stability with strict dissipativity. It is established that the new methodology can reproduce earlier results on passivity, positive realness, and disturbance attenuation. The next section discusses the stabilization of uncertain T–S fuzzy systems with bounded and time-varying input delay using state and observer-based feedback schemes. Extension to T–S fuzzy input delay systems is presented and a separate design principle is developed. Following which a class of fuzzy large-scale nonlinear discrete systems with local quantizers is examined. This fuzzy system has unknown-but-bounded couplings and delays. Of interest are the analysis and design related to decentralized fuzzy feedback structure with \({\mathscr {H}}_\infty \) measure. It is established that the resulting closed-loop fuzzy system exhibits delay-dependent asymptotic stability with disturbance attenuation level. Using quantized output measurements, a local procedure is constructed for tuning the quantizer parameters to achieve similar asymptotic stability and guaranteed performance. The final section investigates new criteria of the robust \({\mathscr {H}}_\infty \) stability of uncertain stochastic fuzzy mixed delay systems with nonlinear noise disturbances by employing an improved free-weighting matrix approach. Both the parameter uncertainties and Brownian motion stochastic disturbances are considered. In terms of a stochastic fuzzy Lyapunov functional, a sufficient criterion is proposed to investigate dynamical behaviors of the system in the mean square sense with an \({\mathscr {H}}_\infty \) performance index.