Optimization Scheme for Stability and Performance Robustness of Uncertain Systems with Structured Uncertainty

It is known that a system subject to structured uncertainty satisfies robust stability if each component of its subsystems is by its own stable for all perturbations less than a maximum bound. It is on the other hand said to have satisfied robust performance if all the functions mapping all subsystem inputs to the corresponding outputs have bounded norms. Here we introduce an optimization scheme that targets robust stability and robust performance for linear time-invariant systems with structured uncertainty in the system and the control (input) matrices. The scheme is formulated such that the eigenvalue spectrums can be clustered in the complex plane within regions satisfying critical constraints defined by Abdul-Wahab and Zohdy [1]. It follows the Riccati equation approach [2] and [3], but with a new structure of the Matrix Riccati Equation (MRE) that leads to a stabilizing controller. The scheme optimizes few parameters formulated from the critical constraints, the stability robust index [3], and the norm of the functions that map system inputs to system outputs [4].