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Semi-global exponential stabilization of linear systems subject to “input saturation” via linear feedbacks. (English) Zbl 0788.93075
Summary: It is known that a linear time-invariant system subject to “input saturation” can be globally asymptotically stabilized if it has no eigenvalues with positive real parts. It is also shown by {\it A. T. Fuller} [(i) Int. J. Control 15, 486-505 (1977)] and {\it H. J. Sussmann} and {\it Y. Yang} [(ii) On the stabilizability of multiple integrators by means of bounded feedback controls, Report SYCON-91-01, Rutgers Center for Systems and Control (1991)] that in general one must use nonlinear control laws and only some special cases can be handled by linear control laws. In this paper, we show the existence of linear state feedback and/or output feedback control laws for semi-global exponential stabilization rather than global asymptotic stabilization of such systems. We explicitly construct linear static state feedback laws and/or linear dynamic output feedback laws that semi-globally exponentially stabilize the given systems. Our results complement the “negative result” of (i) and (ii).

##### MSC:
 93D15 Stabilization of systems by feedback
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##### References:
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