A Simple Switching Control for Linear Systems to Assure Nonovershooting Step Responses

In the paper, we show that for a class of linear plants, although the common linear control can be used to stabilize them, the step responses of the resulting closed-loop systems must have overshoot; however, a simple switching between them may avoid the overshoot. This indicates that switching control may overcome the performance limitation of linear feedback control in the overshoot-avoidance respect. A simple switching control scheme with such a quality is exploited and the conditions for its existence are presented. In the scheme, two common controllers are needed and they are only required to guarantee no overshoot on the time intervals [0, ts) and [ts, ∞), respectively, where ts denotes the switching time. For actual implementation, a state-dependent version of the switching control law is developed. Two examples are presented to show its effectiveness.