An application of semidefinite programming duality to derive bounds on the H/sub /spl infin// norm of a transfer matrix

The problem of computing the H/sub /spl infin// norm of a transfer matrix can be reformulated as a semidefinite program (SDP), by considering a certain quadratic optimal control problem for an associated linear time-invariant system. We apply convex duality theory to this SDP to derive new upper and lower bounds for the H/sub /spl infin// norm.