Optimal controller initialization for switching between stabilizing controllers

An important class of switched systems consists of those systems built as the feedback interconnection of a plant to be controlled, together with a multicontroller whose dynamics switch. When designing this type of switching controllers, one is faced with the questions of how to select controller realizations and how to initialize the state of the controllers as they are switched into the feedback loop. This paper deals with these questions for the problem of switching between linear time- invariant controllers. We show that significant improvements in closed-loop performance can be attained by optimally choosing the initial state of a controller, as this controller is switched into the feedback loop. By including appropriate constraints on the optimizations used to select controller initializations, we show that the resulting switched closed-loop can be made uniformly input-to-state stable for arbitrary switching. Simulations illustrate the benefits of our approach with respect to others previously suggested in the literature.