Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

First Advisor

D. Brett Ridgely, PhD


H2 optimization with convex constraints is considered. The optimal order-free solution is shown to be unique through convex analysis. H constraints with feedforward terms and singular constraints are also allowed. The optimal fixed-order solution is shown to have the same characteristics as a mixed problem with regular H constraints. Furthermore, these results are shown to hold for controller orders as low as the optimal H2 order. A numerical method is developed based on analytical gradients which results in sub- and super-optimal fixed-order controllers. The problem is extended to include an upper bound on a mu constraint through a modification of the D-K iteration method. Next. multiple H constraints are developed. Fixed-order solutions to the multiple constraint problem are characterized and the numerical method is extended to include multiple constraints. Next, a continuous Ll constraint is added. A numerical approach is proposed based on bounding the L1-norm by the 11- norm of an Euler approximating system. Finally. H2 optimization with a finite set of H, mu, and L1 constraints is characterized. SISO and MIMO numerical examples demonstrate the application of these methods.

AFIT Designator


DTIC Accession Number



The author's Vita page is omitted.