Controller design to optimize a composite performance measure

This paper studies a "mixed" objective problem of minimizing a composite measure of the l/sub 1/, /spl Hscr//sub 2/, and l/sub /spl infin// norms together with the l/sub /spl infin// norm of the step response of the closed loop. This performance index can be used to generate Pareto optimal solutions with respect to the individual measures. The problem is analysed for the discrete time, single-input single-output (SISO), linear time invariant systems. It is shown via the Lagrange duality theory that the problem can be reduced to a convex optimization problem with a priori known dimension. In addition, continuity of the unique optimal solution with respect to changes in the coefficients of the linear combination is established.