A CHARACTERIZATION OF ALL SOLUTIONS TO THE 4 BLOCK GENERAL DISTANCE PROBLEM

Journal article

All solutions to the four block general distance problem which arises in H∞ optimal control are characterized. The procedure is to embed the original problem in an all-pass matrix which is constructed. It is then shown that part of this all-pass matrix acts as a generator of all solutions. Special attention is given to the characterization of all optimal solutions by invoking a new descriptor characterization of all-pass transfer functions. As an application, necessary and sufficient conditions are found for the existence of an H∞ optimal controller. Following that, a descriptor representation of all solutions is derived.

Authors: Glover, K; Limebeer, D; Doyle, J; Kasenally, E; Safonov, M

• Publication status: Published
• Journal: SIAM JOURNAL ON CONTROL AND OPTIMIZATION
• Volume: 29
• Issue: 2
• Pages: 283-324
• Publication date: 1991-03-01
• DOI: 10.1137/0329016
• EISSN: 1095-7138
• ISSN: 0363-0129
• Keywords: LINEAR QUADRATIC DIFFERENTIAL GAMES; GENERAL DISTANCE PROBLEMS; INDEFINITE FACTORIZATION; 4 BLOCK PROBLEM; PARROTS THEOREM; NEHARIS THEOREM; INDEFINITE RICCATI EQUATIONS; H-INFINITY OPTIMAL CONTROL