Worst-Case Finite-Frequency H2-Norm Analysis of Uncertain Linear Systems

The H 2 norm is a fundamental design metric in many control applications and it is therefore important to evaluate how it is affected by uncertainties in the model. In the space domain, the H 2 norm is particularly significant when the Pointing Error Source (PES) of a satellite can be approximated by a white noise, which is often the case for microvibrations and acoustic disturbances. The present paper discusses a new method to identify a set of real parametric uncertainties which maximizes (resp. minimizes) the finite-frequency H 2 norm of an uncertain Multiple-Input Multiple-Output (MIMO) linear system. To do so, the analytical expression of the finite-frequency H 2 norm is first approximated as a sum of contributions on a discrete frequency grid. A constrained nonlinear optimization is then performed to maximize (resp. minimize) the so-obtained function. The proposed worst-case finite-frequency H 2 -norm analysis paves the way to a wide range of possible applications, specially when integrated into the Verification and Validation (V&V) process of space missions requiring high pointing performances. The theoretical results derived in the paper are implemented and successfully tested on models of increasing complexity.