Stability and stabilization of periodic piecewise linear systems: A matrix polynomial approach

Stability and stabilization of periodic piecewise linear systems: A matrix polynomial approach In this paper, new conditions of stability and stabilization are proposed for periodic piecewise linear systems. A continuous Lyapunov function is constructed with a time-dependent homogeneous Lyapunov matrix polynomial. The exponential stability problem is studied first using square matricial representation and sum of squares form of homogeneous matrix polynomial. Constraints on the exponential order of each subsystem used in previous work are relaxed. State-feedback controllers with time-varying polynomial controller gain are designed to stabilize an unstable periodic piecewise system. The proposed stabilizing controller can be solved directly and effectively, which is applicable to more general situations than those previously covered. Numerical examples are given to illustrate the effectiveness of the proposed method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Automatica Elsevier

Stability and stabilization of periodic piecewise linear systems: A matrix polynomial approach

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Ltd
ISSN
0005-1098
D.O.I.
10.1016/j.automatica.2018.02.015
Publisher site
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Abstract

In this paper, new conditions of stability and stabilization are proposed for periodic piecewise linear systems. A continuous Lyapunov function is constructed with a time-dependent homogeneous Lyapunov matrix polynomial. The exponential stability problem is studied first using square matricial representation and sum of squares form of homogeneous matrix polynomial. Constraints on the exponential order of each subsystem used in previous work are relaxed. State-feedback controllers with time-varying polynomial controller gain are designed to stabilize an unstable periodic piecewise system. The proposed stabilizing controller can be solved directly and effectively, which is applicable to more general situations than those previously covered. Numerical examples are given to illustrate the effectiveness of the proposed method.

Journal

AutomaticaElsevier

Published: Aug 1, 2018

References

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