A composite performance measure

Abstract

In this chapter we considered a mixed objective problem of minimizing a given linear combination of the l ₁ norm, the square of the H ₂ norm, and the ℓ_∞ norms of the step and pulse responses respectively of the closed loop. Employing the Khun-Tucker-Lagrange duality theorem it was shown that this problem is equivalent to a finite dimensional convex optimization problem with an a priori known dimension. The solution is unique and represents a Pareto optimal point with respect to the individual measures involved. It was also shown that the optimal solution is continuous with respect to changes in the coefficients of the composite measure.