A Riccati equation approach to the optimal guaranteed cost control of uncertain systems with structured uncertainty

In this paper, a Riccati equation approach is presented to construct the optimal quadratic guaranteed cost controller for uncertain systems. The uncertainty in the system is assumed to be norm bounded, time-varying and structured. The Riccati equation depends on a positive definite diagonal matrix. This matrix has the same structure as the uncertainty in the system. The paper presents a definition of convexity for matrix functions. Using this definition, it is proved that the stabilizing solution of the Riccati equation is a convex matrix function of the diagonal elements in the dependent matrix. Therefore, the optimal guaranteed cost controller can be found by carrying out a search with respect to the diagonal elements in the dependent matrix