Abstract
This chapter investigates the problem of robust ℋ∞ piecewise statefeedback control for a class of nonlinear discrete-time-delay systems via Takagi-Sugeno (T-S) fuzzy models. The state delay is assumed to be time-varying and of an interval-like type with the lower and upper bounds. The parameter uncertainties are assumed to have a structured linear-fractional form. Based on two novel piecewise Lyapunov-Krasovskii functionals and some matrix inequality convexifying techniques, both delay-independent and delay-dependent controller design approaches are developed in terms of a set of linear matrix inequalities (LMIs). Numerical examples are also provided to illustrate the effectiveness and less conservatism of the proposed methods.
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