Extended Small Gain Theorem with application to time-delay switched linear systems

Abstract

This paper generalizes the Small Gain Theorem - SGT to cope with time-delay switched linear systems. The main purpose is to obtain delay-dependent stability conditions that can be imposed by means of an appropriate switching strategy. Both cases of switching strategies corresponding to state and output feedback are considered. The new version of SGT is specially important in the framework of switched linear systems because it allows robustness analysis with respect to parameter or frequency domain uncertainty arising in ℋ∞ control problems and constant time-delay modeling. Since only sufficient conditions are given, the conservativeness of the final results is evaluated in terms of the gain promoted by the switching strategy, exclusively. The theory is illustrated by means of academic examples.