In this paper methods are prsented for calculating the maximal parameter pertubation bounds under H2 performance constraints for a family of uncertain systems and for calculating the average H2 performance under such parameter variations. The uncertain systems are described by state space models with nonlinear (polymnial) dependencies on real uncertain parameters. All results obtained are based on necessary and sufficient conditions. As a special virtue of the approach the proposed algorithms for stability analysis and for performance analysis turn out to have exactly the same algebraic structure. An example illustrates the results and the algorithms.
Zhao, K-Y., Grimble, M. J., & Stoustrup, J. (1999). Average H2 performance and maximal parameter pertubation radius for uncertain systems. SIAM Journal on Control and Optimization, 1742-1750. https://doi.org/10.1137/S0363012996301725