Filtering for Switched T–S Fuzzy Systems With Persistent Dwell Time

The <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mathcal {H}_{\infty }}$ </tex-math></inline-formula> filter design for a class of switched Takagi–Sugeno (T–S) fuzzy systems with persistent dwell time (PDT) is investigated in this paper. The considered switched fuzzy systems contain a limited number of subsystems and each local subsystem is represented by the well-known T–S fuzzy model. Compared with the dwell time (DT) switching or average DT switching that attracted quantities of interests over the last decade, the PDT switching considered in this paper is known to be more general. The stability and <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mathcal {L} _{2}}$ </tex-math></inline-formula>-gain analysis for switched systems with PDT switching are derived first, based on which a set of full-order <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mathcal {H}_{\infty }}$ </tex-math></inline-formula> filter is designed to guarantee the global uniform asymptotic stability with a prescribed nonweighted <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mathcal {H}_{\infty }}$ </tex-math></inline-formula> noise attenuation performance for the resulting filtering error system. Finally, the effectiveness of the provided method is illustrated with an example.