Robust Switching Control: Stability Analysis and Application to Active Disturbance Attenuation

This note deals with the problem of controlling an uncertain discrete-time linear system by means of a hybrid controller in the form of a linear system whose parameters switch among a finite number of possible configurations, called modes. We suppose that each single controller is designed in order to individually ensure robust stability for a dual-Youla uncertainty model. Then, we show that robust stability of the switching controller can be directly related to robust stability of each single controller mode, in that it is possible to implement the switching controller so that robust stability is guaranteed for any possible switching sequence. This allows one to freely select the switching signal so as to enhance performance, for instance by selecting in real time the control mode displaying the best potential performance with respect to the current operating conditions. An application of the ideas to the problem of active disturbance attenuation is presented and simulation results are shown to validate the proposed solution.