Finite frequency H_∞ control for 2-D T-S fuzzy FM II model with stochastic perturbation

ABSTRACT

The design of $H_{\mathrm{\infty }}$ control for two-dimensional (2-D) Takagi-Sugeno (T-S) fuzzy systems with stochastic perturbation described by the second Fornasini-Marchesini (FM II) model has been solved in this paper. With the aid of the Generalised Kalman Yakubovich-Popov (GKYP) Lemma, sufficient conditions of the existence of the finite frequency (FF) $H_{\mathrm{\infty }}$ control are presented, in the form of linear matrix inequalities (LMIs). New conditions guaranteeing finite frequency of the closed-loop systems are further derived to design $H_{\mathrm{\infty }}$ fuzzy control, where state-feedback control law is considered. Moreover, the proposed conditions provide less conservative results than those derived from existing ones. Some examples are fully developed to show the applicability of the proposed design approach.

Keywords:

• Takagi-Sugeno fuzzy systems
• finite frequency $H_{\mathrm{\infty }}$
• 2-D T-S fuzzy FM II model
• stochastic perturbation

Disclosure statement

No potential conflict of interest was reported by the authors.