Analysis of Discrete-time H2 Guaranteed Cost Performance

This paper presents a methodology for analyzing the H2 guaranteed cost performance of a discrete-time LTI system with unstructured dynamic uncertainty. Using the methods of guaranteed cost control, an upper bound on H2 guaranteed cost performance over unstructured parametric uncertainty is formulated in terms of feasibility of a linear matrix inequality. It is then shown that the feasibility of this inequality also guarantees the same level of performance also over unstructured dynamic uncertainty. This is then used to formulate the problem of finding the best upper bound on H2 guaranteed cost performance over unstructured causal dynamic uncertainty as a semi-definite program. Finally, it is shown that this optimization problem can be solved efficiently and accurately using discrete algebraic Riccati equations.