Switching PDC control for discrete-time T–S fuzzy system: A membership function ranking approach

In this paper, a new type of switched parallel distributed compensation (PDC) controller is presented, in which a novel switching scheme, namely, membership function ranking (MFR) scheme is proposed. The MFR scheme can be viewed as an improvement and extension of previous results named largest membership function (LMF) scheme concerned with piece-wise quadratic Lyapunov function (PQLF) approach, since it provides a denser subdivision of normalized membership function space and therefore essentially yields less conservative results. Moreover, it shows that MFR scheme covers LMF scheme as a particular case. Based on MFR scheme, a family of ℋ ∞ controllers and a switching scheme is designed to ensure the closed-loop system asymptotically stable and has a required ℋ ∞ performance. A design example is presented to illustrate the advantages of MFR scheme.