Analysis and synthesis for linear set-valued dynamically varying systems

The analysis and synthesis for linear systems with parameters that vary according to a set-valued map are investigated. It is shown that the optimal controllers are continuous and homogeneous, but not additive. A computational method based on approximating the nonquadratic cost by a piecewise quadratic function is developed. Such an approximation determines stability nonconservatively and preserves the homogeneity of the controller. Computational methods for both analysis and synthesis are provided