Convexity vs. compensator order for the discrete-time, mixed-norm control problem

This paper address the issues of convexity and compensator order in mixed-norm optimization. The optimal H₂/l₁ control problem is formulated as a convex problem, and result in a compensator which is of arbitrarily high order. Because it is usually impractical to implement a very high order compensator, a fixed-order method is used to find compensators of a specifiable order. However, the fixed-order method results in a non-convex optimization problem in which there are local minima. The non-convexity and local minima resulting from the fixed-order problem are examined using the Pareto-optimal H₂/l₁ curves and compensator eigenvalue traces for varying compensator order. It is shown that it requires a discontinuous jump in the design variables to move from one local minimum to another. While these discontinuities can cause problems, several methods for dealing with them are suggested