From Mixed to Multi-Objective Control

We revisit a technique for solving multi-objective control problems through aanely parameterizing the closed-loop system with the Youla parameterization and conning the search of the Youla parameter to nite-dimensional subspaces. It is pretty well-known how to solve such problems if the closed-loop speciication are formulated in terms of the solvability of linear matrix inequalities. However, all approaches proposed so far suuer from a substantial innation of size of the resulting optimization problems if improving the approximation accuracy. On the basis of a novel state-space approach to solve static output feedback control problem by convex optimization for a speciic class of plants, we reveal how the innation of the size of the optimization problems can be avoided to arrive at more eecient algorithms. As an additional ingredient we discuss how to use a so-called mixed controller as a starting point for a genuine multi-objective design in order to improve the algorithms. Notation. All plants are described in discrete-time, and a (transfer) matrix is said to be stable if all its (poles) eigenvalues are contained in the open unit disk. For A 2 C nm , kAk F denotes the Frobenius norm kAk the spectral norm of A. RH 1 denotes the set of all proper and stable transfer matrices. This algebra is equipped either with the H 2-norm kTk 2 2 = 1 2 R 2 0 kT(e it)k F dt or the H 1-norm kTk 1 = max t20;2] kT(e it)k: