A Solvability Condition of General Robust Control Problems

Abstract

This paper is concerned with the robust well-posedness problem which is an extension of a general robust control problem. We derive a new solvability condition of the problem in the form of a linear matrix inequality (LMI) condition adding a rank condition. The condition is still non-convex due to the existence of the rank condition. However, it can be checked approximately with the alternating projection method, and the approach might be more efficient than the existing methods from the viewpoint of computation.