Exponential stabilization of discrete-time switched linear systems |
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Authors: | Wei Alessandro Jianghai Michael P |
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Affiliation: | aDepartment of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47906, USA;bDepartment of Aeronautics and Astronautics, Stanford University, CA 94305, USA |
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Abstract: | This article studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov function approach. It is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control-Lyapunov function. Such a converse control-Lyapunov function theorem justifies many of the earlier synthesis methods that have adopted piecewise quadratic Lyapunov functions for convenience or heuristic reasons. In addition, it is also proved that if a switched linear system is exponentially stabilizable, then it must be stabilizable by a stationary suboptimal policy of a related switched linear-quadratic regulator (LQR) problem. Motivated by some recent results of the switched LQR problem, an efficient algorithm is proposed, which is guaranteed to yield a control-Lyapunov function and a stabilizing policy whenever the system is exponentially stabilizable. |
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Keywords: | Switched systems Piecewise quadratic Lyapunov functions Switching stabilization Optimal control Control-Lyapunov functions |
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