Stability and stabilization for a class of polynomial discrete fuzzy systems with time delay by sum-of-squares optimization

The paper presents stability and stabilization conditions of a class of polynomial discrete fuzzy systems with time delay, using the sum-of-squares (SOS) approach. First, through employing a parameter dependent discrete Lyapunov-Krasovskii functional, with some free weighting matrices, a delay-dependent stability criterion is obtained. Next, Based on the fuzzy control approach (PDC), controller synthesis can be done. Both of them are represented in terms of SOS, which can be efficiently solved via the recent developed SOSTOOLS. Simulation examples are given to verify the stability analysis results and demonstrate the effectiveness of controller design method.