| Summary: | In this paper, the stability problem for the digital redesign of discrete-time switched systems using <i>H<sub>∞</sub></i> linear matrix inequality (LMI) is investigated. We propose the switching time approach for digital redesign between controller work and failure, and this switching time will limit the system output within the system capacity. When the controller fails, the overall system will be unstable. Therefore, if the digital redesign controller is not restored in a certain period of time, the system output will exceed the system capacity. To solve this problem, we propose a switching law to determine the switching time between the stable mode (controller work) and the unstable (controller failure) mode; this will limit the overall system states in the unstable mode. In addition, the digital redesign controller has the advantage of faster tracking. After we propose a discrete-time switching system with stable and unstable modes, we use <i>H<sub>∞</sub></i> linear matrix inequality (LMI) and Lyapunov functions to prove the stability in detail. Finally, the numerical example illustrates the feasibility of the proposed approach.
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