Abstract
The problem of controller design with variance and circular pole constraints is considered in this paper. The motivation for this problem is twofold: (1) many engineering systems have performance requirements naturally stated in terms of upper bounds on the variances of the system states; and (2) the fine transient properties of the closed-loop system are required in practice. The goal of this problem is to design the controller such that the closed-loop system meets the prespecified variance constraints and circular pole constraints simultaneously. It is shown that a desired controller is determined by using the solution of a modified Lyapunov equation. Necessary and sufficient conditions are given for the existence of desired controllers. The set of desired controllers (if they exist) is also characterized.
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