Switched PD-like Controllers for First Order Unstable Systems with Time Delay

A new method is proposed for the design of PD-like (first order stable) controllers for switched first order unstable systems with time delays. For this purpose, a dwell-time based stability condition of Yan and Özbay (2008) is used for the class of switched time delay systems studied here. The proposed method finds the values of PD-like controller parameters which minimize an upper bound of the dwell time, minimum time needed between the switching instants to preserve stability. The conservatism analysis of this method is done by time domain simulations. The results show that the calculated upper bound for the dwell time is close to the lower bound of the dwell time observed by simulations.