Time-varying problems of H∞ control and absolute stabilizability of uncertain systems

This paper considers an absolute stabilization problem for a class of time-varying uncertain systems in which the uncertainty satisfies an integral quadratic constraint. The main result of the paper shows that a state feedback absolute stabilization problem has a solution if and only if there exists a solution to a corresponding infinite horizon, time-varying, state feedback H^∞ control problem. The paper also shows that if either of these problems can be solved via the use of nonlinear state feedback control then it can also be solved via the use of linear state feedback control. Furthermore, the required controller can be constructed by solving a Riccati differential equation. The paper also considers the special case of periodic time-varying systems.