An exact solution to general SISO mixed ℋ/sub 2//ℋ/sub ∞/ problems via convex optimization

Abstract

The mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin// control problem can be motivated as a nominal LQG optimal control problem, subject to robust stability constraints, expressed in the form of an /spl Hscr//sub /spl infin// norm bound. A related modified problem consisting on minimizing an upper bound of the /spl Hscr//sub 2/ cost subject to /spl Hscr//sub /spl infin// constraints was introduced by Bernstein-Haddad (1989). Although there presently exist efficient methods to solve this modified problem, the original problem remains, to a large extent, still open. In this paper we propose a method for solving general discrete-time SISO /spl Hscr//sub 2///spl Hscr//sub /spl infin// problems. This method involves solving a sequence of problems, each one consisting of a finite-dimensional convex optimization and an unconstrained Nehari approximation problem.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>