Strictly Positive Real H Controller Synthesis via Iterative Algorithms for Convex Optimization

Abstract

The synthesis of strictly positive real H 2 controllers for collocated control of large space structures is addressed. To perform this synthesis, a convex optimization technique has already been developed using linear matrix inequalities. This existing technique is based on two design criteria: strict positive realness and the use of H 2 norm as the criterion for optimization. It adopts a common Lyapunov solution to both of these criteria, which results in undesirable conservatism. To reduce this conservatism, a new synthesis technique based on iterative algorithms that can produce superior, noncommon Lyapunov solutions is proposed. Even if a common Lyapunov solution is infeasible, the proposed technique can yield feasible, strictly positive real H 2 controllers. An illustrated example is included.