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

摘要

In this paper, a Riccati equation approach is presented toconstruct the optimal quadratic guaranteed cost controller for uncertainsystems. The uncertainty in the system is assumed to be norm bounded,time-varying and structured. The Riccati equation depends on a positivedefinite diagonal matrix. This matrix has the same structure as theuncertainty in the system. The paper presents a definition of convexityfor matrix functions. Using this definition, it is proved that thestabilizing solution of the Riccati equation is a convex matrix functionof the diagonal elements in the dependent matrix. Therefore, the optimalguaranteed cost controller can be found by carrying out a search withrespect to the diagonal elements in the dependent matrix