On controller initialization in multivariable switching systems

We consider a class of switched systems which consists of a linear MIMO and possibly unstable process in feedback interconnection with a multicontroller whose dynamics switch. It is shown how one can achieve significantly better transient performance by selecting the initial condition for every controller when it is inserted into the feedback loop. This initialization is obtained by performing the minimization of a quadratic cost function of the tracking error, controlled output, and control signal. We guarantee input-to-state stability of the closed-loop system when the average number of switches per unit of time is smaller than a specific value. If this is not the case then stability can still be achieved by adding a mild constraint to the optimization. We illustrate the use of our results in the control of a flexible beam actuated in torque. This system is unstable with two poles at the origin and contains several lightly damped modes, which can be easily excited by controller switching.