Abstract
The paper is concerned with the stabilization of positive periodic piecewise linear systems composed of not all Hurwitz stable subsystems. By employing a periodic time-segment based time-varying linear copositive Lyapunov function, a less conservative stability condition for the exponential stability of the underlying systems is obtained, which can be checked via linear programming. Efficient periodic time-segment based time-varying controller design methods are developed such that the closed loop system is not only positive but also exponentially stable. Finally, the theoretical results obtained are demonstrated by a numerical example.
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