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It is known that for single-input neutrally stable planar systems, there exists a class of saturated globally stabilizing linear state feedback control laws. The goal of this paper is to characterize the dynamic behavior for such a system under arbitrary locally stabilizing linear state feedback control laws. On the one hand, for the continuous-time case, we show that all locally stabilizing linear...
This paper further studies the discrete-time double integrator. Earlier it has been shown by us that there exists a class of locally stabilizing saturated linear state feedbacks which cause periodic behavior for certain initial conditions and hence the closed-loop system is then not globally asymptotically stable. In this paper, we show that all the remaining locally stabilizing saturated linear state...
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