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Quadratic stabilizability of switched linear systems with polytopic uncertainties. (English) Zbl 1034.93055
The authors discuss quadratic stabilizability via state feedback for both continuous-time and discrete-time switched linear systems that are composed of polytopic uncertain subsystems. For a continuous-time switched linear system, the authors show that if there exists a common positive definite matrix for the stability of all convex combinations of the extreme points which belong to different subsystem matrices, then the switched system is quadratically stabilizable via state feedback. For discrete-time switched linear systems, the authors derive a quadratic stabilizability condition expressed as matrix inequalities with respect to a family on nonnegative scalars and a common positive definite matrix. In addition the authors give switching rules using the common positive definite matrix for both continuous-time and discrete-time switched systems.

MSC:
93D15 Stabilization of systems by feedback
93B12 Variable structure systems
93D09 Robust stability
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