Quadratic Stabilizability of Switched Linear Systems with Polytopic Uncertainties

G. Zhai, (Japan), H. Lin and P. Antsaklis (USA)


Continuous-time switched system, discrete-time switched system, quadratic stabilizability, switching rule, state feedback, matrix inequality.


In this paper, we consider quadratic stabilizability via state feedback for both continuous time and discrete-time switched linear systems that are composed of polytopic uncertain subsystems. By state feedback, we mean that the switchings among subsystems are dependent on system state. For continuous-time switched linear systems, we show that if there exists a common positive definite ma trix for 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, we derive a quadratic stabilizability condition expressed as matrix inequalities with respect to a family of nonnegative scalars and a common positive definite matrix. For both continuous-time and discrete-time switched systems, we establish the switching rules by using the common positive definite matrix.

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