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Reliable $H_\infty $ control for discrete-time piecewise linear systems with infinite distributed delays. (English) Zbl 1192.93030
Summary: The reliable $H_\infty $ control problem is investigated for discrete-time piecewise linear systems with time delays and actuator failures. The time delays are assumed to be infinitely distributed in the discrete-time domain, and the possible failure of each actuator is described by a variable varying in a given interval. The aim of the addressed reliable $H_\infty $ control problem is to design a controller such that, for the admissible infinite distributed delays and possible actuator failures, the closed-loop system is exponentially stable with a given disturbance attenuation level $\gamma $. The controller gain is characterized in terms of the solution to a linear matrix inequality that can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.

93C55Discrete-time control systems
93C05Linear control systems
93D20Asymptotic stability of control systems
Full Text: DOI
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