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Existence of a common quadratic Lyapunov function for discrete switched linear systems with m stable subsystems

Existence of a common quadratic Lyapunov function for discrete switched linear systems with m stable subsystems

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The problem on the existence of a common quadratic Lyapunov function (CQLF) for discrete switched linear systems with m stable subsystems is considered. System matrices are Schur stable. A necessary condition for the existence of a CQLF and a sufficient condition for the non-existence of a CQLF are derived, respectively. Numerical examples are presented to illustrate the results.

References

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      • Shorten, R.N., Narendra, K.S.: `Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for m stable second order linear time-invariant systems', Proc. American Control Conf., June 2000, Chicago, IL, p. 359–363.
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