Stability Analysis - Multiconvexity Approach

Recently a large number of literature on fuzzy control are TS model-based control where, mostly, the common P approach searching for a single Lyapunov function remains active Wang et al. [1996], Tanaka et al. [1998], Kim and Lee [2000], Blanco et al. [2000], Tuan et al. [2001]. Another category emphasizes parameter-dependent functions with multiple Pj matrices as a candidate of Lyapunov function Johansson et al. [1999], Kiriakidis [2001], Chadli et al. [2000], Tanaka et al. [2001a,b], Feng and Ma [2001], Cao et al. [1996]. To remove the time-derivative dependence, progress has been made recently in obtaining less conservative results using non-quadratic approach (multiple Lyapunov functions) Morere et al. [1999], Guerra and Perruquetti [2001], Guerra and Vermeiren [2001], Tanaka et al. [2003] where a fuzzy Lyapunov candidate is used for a discreteand continuous-time T-S fuzzy model and the resulting stability condition is shown to be more relaxed than the condition derived from the common P approach. In this paper, multiconvexity property from Apkarian and Tuan [2000] is combined with premise-dependent Lyapunov function to derive sufficient conditions for stability test of TS fuzzy systems.