Biblio

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.

We address a discrete-time LQG control problem over a fixed performance window and apply a receding-horizon type control strategy, resulting in an exact solution to the problem in terms of semidefinite programming. The systems considered take parameters from a finite set, and switch between them according to an automaton. The controller has a finite preview of future parameters, beyond which only the set of parameters is known. We provide necessary and sufficient convex con- ditions for the existence of a controller which guarantees both exponential stability and finite-horizon performance levels for the system; the performance levels may differ according to the particular parameter sequence within the performance window. A simple, physics-based example is provided to illustrate the main results.