Stability analysis and design of reset control systems with discrete-time triggering conditions

In a reset control system, reset actions are usually triggered whenever a continuous signal crosses a hyperplane. In the computer-based implementation, however, the continuous triggering signal is sampled and the triggering condition is then replaced by a discrete-time counterpart. In this work, we are concerned with the stability analysis and design of reset control systems based directly on discrete-time triggering conditions. First, a relationship between reset control systems and switched systems is established and some stability criteria are then obtained. Second, it is revealed through an example that a well-designed reset control system can be regarded as a hybrid system combining an underdamped baseline system with an overdamped reset mode. The reset matrix, which is assumed to be zero in general, can be adjusted to increase the damping ratio and thus further improve the transient performance. Based on this observation, a design guideline for single-input and single-output (SISO) systems is proposed. Lastly, a hard disk drive example is investigated to demonstrate the proposed design procedure.