On the Stabilizability of Control Constrained Linear Systems
We study the problem of stabilization of time-invariant linear systems with controls which are constrained in a cone. Under small-time local controllability conditions we propose a simple construction of a Lipschitz piecewise linear stabilizing feedback. Moreover, we show that the stabilizing feedback can be chosen in such a way that the number of switchings from one linear form to another, that may occur along a trajectory of the closed-loop system, is uniformly bounded.
KeywordsConvex Cone Linear Feedback Closed Convex Cone Admissible Trajectory Polyhedral Convex Cone
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