Stabilization of Linear Systems with Time-Varying Delays

Abstract

In this chapter, we extend the preceding stabilization results to linear systems with time-varying delays. The extension is rendered possible by the operator-theoretic approaches developed in Chaps. 3 and 4: While the small-gain stability conditions are developed in Chap. 3 for systems with time-varying delays, the interpolation approach used in Chap. 4 enables us to address stabilization problems directly based on the small-gain conditions. This insures that the results on the delay margin can be cohesively extended, and in a unified manner. Indeed, it will be seen that bulk of the results in Chap. 4 can be used to address the stabilization of systems with time-varying delays, modulo to some minor modifications. Efficient computational formulas and analytical expressions are also obtained, which incorporate the time-varying delay characteristics of delay range and delay variation rate.