A MATLAB toolbox for fixed order, mixed-norm control synthesis

This paper introduces a MATLAB toolbox for fixed order, mixed-norm control synthesis. The Mixed-Norm Toolbox contains a complete set of routines for both continuous and discrete-time systems. The problem addressed by the toolbox is that of finding a compensator which minimizes the H₂ norm of a transfer function, while constraining any combination of H_∞ and/or l₁ (L₁) norms of possibly dissimilar transfer functions to be below specified levels. Within reason, any number or combination of constraints can be added to the problem, and the method constrains the norms directly without reliance on upper bounds. The primary contribution of the Mixed-Norm Toolbox is a modular collection of norm and gradient algorithms which can be used with almost any non-linear, constrained optimization solver. While global convergence is not guaranteed for the resulting non-convex problem, the toolbox has been successfully used to show portions of Pareto optimal curves and surfaces for a wide variety of problems. The Mixed-Norm Toolbox is being made available free of charge to the controls community