Abstract
We investigate the design of periodic stabilizing switching signals for compartmental switched systems in both the continuous-time and discrete-time framework. For a continuous-time compartmental switched system, we fully characterize the class of periodic stabilizing switching signals. Specifically, a periodic switching signal is stabilizing if and only if the sum of the subsystem matrices appearing during one period is Hurwitz. For the discrete-time counterpart, we point out that the zero/nonzero structure of the diagonal elements of the subsystem matrices is vital in the design of periodic stabilizing switching signals. To be specific, when all the diagonal elements of the subsystem matrices are positive, a periodic switching signal is stabilizing if and only if the average of the subsystem matrices appearing during one period is Schur. Such a result may not hold when zero appears in some diagonal positions of some subsystem matrices.
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