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

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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.

Inspec keywords: linear systems; Lyapunov methods; stability; discrete systems; matrix algebra

Other keywords: common quadratic Lyapunov function; Schur stable system matrix; m stable subsystem; discrete switched linear system

Subjects: Discrete control systems; Algebra; Stability in control theory

References

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