Guaranteed cost controller design for discrete-time switching fuzzy systems

With two level weighting functions, namely, crisp switching-region weighting functions and local fuzzy weighting functions, this paper introduces a discrete-time switching fuzzy system, which inherently contains the features of switched hybrid systems and Takagi-Sugeno (TS) fuzzy systems, and then, for this discrete-time switching fuzzy system, this paper proposes two new guaranteed cost state-feedback controllers minimizing an upper bound of state and input energy called LQ performance under all admissible grades of time-varying fuzzy weighting functions. The first one, associated with a piecewise quadratic Lyapunov function (PQLF), uses time-varying information on the switching-region weighting functions. The second one, associated with a new piecewise fuzzy weighting-dependent Lyapunov function (PFWLF), uses time-varying information on the local fuzzy weighting functions as well as on the switching-region functions. Especially with a new special structure of the candidate of PFWLF, the PFWLF-based controller employs not only the current-time but also the one-step-past information on the time-varying local fuzzy weighting functions.