$H^\infty $ Control of Linear Time-Varying Systems: A State-Space Approach

Abstract

In this paper the standard problem of $H^\infty $ control theory for finite-dimensional linear time-varying continuous-time plants is considered. The problem is: given a real number $\gamma > 0$, find (if one exists) an internally stabilizing controller such that the closed-loop operator norm is less than $\gamma $. Under rather weak assumptions on the plant model, it is shown that a solution to this problem exists if and only if a pair of matrix Riccati differential equations admits positive semidefinite stabilizing solutions. State-space formulae for one solution to the problem are also given.