Reset control systems with time-delays

A reset controller, as the name suggests, is no more than a standard controller endowed with a reset-mechanism. This kind of controllers was the first attempt to overcome fundamental limitations of linear control systems. Stability of reset time delay systems can be addressed based on a theorem extending Lyapunov-Krasovskii theory. In this chapter, a robust delay-dependent stability analysis of reset control systems is developed for linear time-invariant systems. The conditions of stability are given in terms of linear matrix inequalities. In addition, the results are extended to investigate the stability of observer based reset control systems with delay. A numerical example is used to illustrate the effectiveness of the proposed approach.