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Robust stability of discrete bilinear uncertain time-delay systems. (English) Zbl 1238.93076
Summary: This paper addresses the problem of robust stability for discrete homogeneous bilinear time-delay systems subjected to uncertainties. Two kinds of uncertainties are treated: (1) nonlinear uncertainties and (2) parametric uncertainties. For parametric uncertainties, we also discuss both unstructured uncertainties and interval matrices. By using Lyapunov’s stability theorem associated with some linear algebraic techniques, several delay-independent criteria are developed to guarantee the robust stability of the overall system. One of the features of the newly developed criteria is its independence from the Lyapunov equation, although the Lyapunov approach is adopted. Furthermore, the transient response and the decay rate of the resulting systems are also estimated. In particular, the transient responses for the aforementioned systems with parametric uncertainties also do not involve any Lyapunov equation which remains unsolved. All the results obtained are also applied to analyze the stability of uncertain time-delay systems.

93D09 Robust stability
93C55 Discrete-time control/observation systems
93C10 Nonlinear systems in control theory
Full Text: DOI
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