Stabilizing design for discrete-time reversible switched linear control systems: A deadbeat control approach

Abstract In this work, we address the feedback stabilization problem for discrete-time reversible switched linear control systems. We focus on the question “how many state feedback gain matrices are needed for an n th order system with m subsystems?” We prove that n + m is an upper bound for the question. For completely controllable systems , a constructive design scheme is developed to steer any initial state to the origin within n ( n + 1 ) 2 steps. When the controllability is incomplete, we prove that the system is stabilizable iff the uncontrollable sub-mode is stabilizable, and propose a mixed time-driven and state-driven switching law to stabilize both the controllable sub-mode and the uncontrollable sub-mode simultaneously.

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