Control of Linear Switched Systems with Receding Horizon Modal Information

We provide an exact solution to two performance problems--one of disturbance attenuation and one of windowed variance minimization--subject to exponential stability. Considered are switched systems, whose parameters come from a finite set and switch according to a language such as that specified by an automaton. The controllers are path-dependent, having finite memory of past plant parameters and finite foreknowledge of future parameters. Exact, convex synthesis conditions for each performance problem are expressed in terms of nested linear matrix inequalities. The resulting semidefinite programming problem may be solved offline to arrive at a suitable controller. A notion of path-by-path performance is introduced for each performance problem, leading to improved system performance. Non-regular switching languages are considered and the results are extended to these languages. Two simple, physically motivated examples are given to demonstrate the application of these results.