Abstract
In this work, we address both the state feedback stabilization problem and the dynamic output feedback stabilization problem for third-order continuous-time switched linear systems. Based on the controllability normal form decomposition approach, we prove that any controllable system is state feedback stabilizable, and the rate of convergence could be arbitrarily pre-assigned. Furthermore, for observable switched systems, we propose a reduced-order observer that could asymptotically estimate the unmeasured states. The dynamic output feedback stabilization problem is solved by designing a common switching law that stabilizes both the state and the observer. The design process is completely constructive.
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