Nonquadratic Lyapunov function based control law design for discrete fuzzy systems with state and input delays

This paper deals with the stability analysis and the stabilization control law for a class of discrete Takagi-Sugeno (T-S) fuzzy systems with both state and input delays. Based on the nonquadratic Lyapunov function constructed here, the stability analysis and the design way of stabilization control law are derived in the form of linear matrix inequality (LMI) via a nonparallel distributed compensation (non-PDC) scheme. The new conclusion is also suitable for a PDC law under a special situation. Two numerical examples are supplied to demonstrate the effectiveness of the designed control law. And both theoretical analysis and numerical examples illustrate that these novel sufficient conditions are less conservative than previous results obtained within the quadratic framework.