L2-Gain Stability Analysis via LMIs for Polytopic Systems with Sector-Bounded Memoryless Nonlinearities

This paper considers L 2 -gain analysis for uncertain linear time-invariant systems with polytopic uncertainties interconnected with sector-bounded static memoryless nonlinearities. A finite set of sufficient Linear Matrix Inequalities (LMIs) is derived by leveraging the polytopic structure to compute upper bounds on the system’s L 2 -gain without requiring gridding or approximation methods. The practical utility of these results is demonstrated through numerical experiments using a benchmark two-mass spring-damper system and a metastructure, exploring relationships among sector bounds, uncertainty levels, and achievable performance.