H∞ control with outputweights for descriptor systems: An LMI approach

This paper deals with a nonstandard H_∞ control problem for continuous-time descriptor systems with unstable and nonproper output weighting functions. In this problem, a desired controller is sought to render the closed-loop system comprehensively admissible and achieve some prescribed H_∞ performance for the closed-loop system as well. By a generalized Sylvester equation, the comprehensive admissibility objective is achieved using a specific structured controller. Thanks to this structured controller, the defined nonstandard control problem can be reduced to a standard H_∞ control problem for an associated descriptor plant. A numerically tractable solution is then derived in terms of a set of linear matrix inequalities (LMIs).