Abstract
This paper studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov function approach. A number of versions of converse control-Lyapunov function theorems are proved and their connections to the switched LQR problem are derived. It is shown that the system is exponentially stabilizable if and only if there exists a finite integer N such that the N-horizon value function of the switched LQR problem is a control-Lyapunov function. An efficient algorithm is also proposed which is guaranteed to yield a control-Lyapunov function and a stabilizing strategy whenever the system is exponentially stabilizable.
This work was partially supported by the National Science Foundation under Grant CNS-0643805.
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Zhang, W., Abate, A., Hu, J. (2009). Stabilization of Discrete-Time Switched Linear Systems: A Control-Lyapunov Function Approach. In: Majumdar, R., Tabuada, P. (eds) Hybrid Systems: Computation and Control. HSCC 2009. Lecture Notes in Computer Science, vol 5469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00602-9_29
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DOI: https://doi.org/10.1007/978-3-642-00602-9_29
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