Stability analysis and design of reset systems: Theory and an application

This paper investigates stability analysis and design of reset control systems where the reset time instants are pre-specified. Firstly, in order to quantify stability of reset control systems, we propose an approach which does not rely on the stability of base linear systems. Based on this, some Lie-algebraic conditions for stability of reset control systems are obtained. Then, we develop a method for reset law design which aims at improving transient responses of the base linear systems. In addition, observer-based design is also considered. We prove that under some mild conditions, reset controller and observer can be designed separately. The obtained results are applied to short-span-seeking control of a kind of single stage hard disk drive servo systems. Simulations show that the proposed design is much more capable of improving transient response than traditional control design techniques.