Stability of Switched Feedback Time-Varying Dynamic Systems Based on the Properties of the Gap Metric for Operators

Abstract

The stabilization of dynamic switched control systems is focused on and based on an operator-based formulation. It is assumed that the controlled object and the controller are described by sequences of closed operator pairs $\mathrm{(L,C)}$ on a Hilbert space $H$ of the input and output spaces and it is related to the existence of the inverse of the resulting input-output operator being admissible and bounded. The technical mechanism addressed to get the results is the appropriate use of the fact that closed operators being sufficiently close to bounded operators, in terms of the gap metric, are also bounded. That philosophy is followed for the operators describing the input-output relations in switched feedback control systems so as to guarantee the closed-loop stabilization.