Stability analysis and controller design of discrete-time polynomial fuzzy time-varying delay systems

This paper investigates the stability and stabilization problems for discrete-time polynomial systems with time-varying delay via a sum of squares (SOS) approach. Unlike the most existing literature, the delayed state is also considered in the controller design. By constructing a new parameter-dependent Lyapunov-Krasovskii function and introducing some free weighting matrices, some novel delay-dependent stability and stabilization conditions are obtained. Then, the results are extended to discrete time-delay systems with norm-bounded uncertainties. The conditions proposed are all derived in terms of SOS, which are more effective than the LMI method in some cases. All the results can be symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program (SDP) solver, respectively. Three numerical examples are provided to demonstrate the effectiveness and superiority of the proposed analysis and design methods.