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Quadratic stabilisation via state and output feedback for continuous-time switched linear systems is studied with the use of a linear matrix inequality (LMI) approach. LMI-based conditions are established for both a state feedback case and an observer-based output feedback case. Under these conditions, the switched linear systems are quadratically stabilisable via either a state-based or a measurable output-based switching strategy. A sufficient and necessary LMI-based condition is also obtained for the state feedback case when there are only two subsystems in the switched linear systems. These results are extended to uncertain switched systems.
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Ji et al. (2004) studied this question.
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