Optimal, constant I/O similarity scaling for full-information and state-feedback control problems

Abstract

In robust control problems, capturing all robustness and performance objectives in a single H ∞ norm cost function is impossible. An alternative approach, still untilizing the H ∞ norm, involves diagonal similarity scaling of certain closed loop transfer functions. The set of allowable diagonal scalings is problem dependent, and reflects assumptions about the uncertainty, and desired performance objectives. The scaling set considered here is a prescribed convex set of positive definite matrices. We consider the optimal constant scaling problem for the Full-Information H ∞ control problem. The solution is obtained by transforming the original problem into a convex feasibility problem, specifically, a structured, linear matrix inequality. In special cases, solvability of the Full-Information problem is equivalent to solvability of the State-Feedback problem.