Stability Analysis and Controller Design for Discrete-Time Fuzzy Systems With Time-Varying Delay

Convex conditions for stability analysis and control synthesis for discrete-time fuzzy systems with time-varying delay are proposed in this paper. The conditions depend on the variation rate of the time-delay and are obtained by considering a parameter dependent Lyapunov-Krasovskii functional. To reduce the conservatism, besides the standard techniques to include extra matrix variables, some extra equations related to the control signal are also added. It is shown that this approach leads to a less expensive convex formulation that the standard way. In all cases, the conditions are formulated as an LMI (linear matrix inequality) feasibility test, that can be efficiently solved in polynomial time by specialized numerical solvers. Numerical examples are presented to compare and illustrate the efficiency of the proposed conditions.