Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities. (English) Zbl 1209.93128

Summary: The problem of global asymptotic stability analysis and controller synthesis for a class of discrete linear time-delay systems with state saturation nonlinearities is investigated. With the introduction of a free matrix whose infinity norm is less than or equal to 1, the state of discrete linear time-delay systems with state saturation is bounded by a convex hull, which makes it feasible to apply a suitable Lyapunov functional to obtain a sufficient condition for global asymptotic stability. It is also shown that this condition can be extended to controller synthesis and discrete time-delay systems with partial state saturation. The obtained results are expressed in terms of matrix inequalities that can be solved by the presented iterative linear matrix inequality approach. The effectiveness of these results is demonstrated by some numerical examples.


93D20 Asymptotic stability in control theory
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
93B50 Synthesis problems
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