Robust stability and stabilization of uncertain linear positive systems via Integral Linear Constraints : L 1-and L ∞-gains characterization

Copositive linear Lyapunov functions are used along with di ssipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for robustness and performance analysis using L1and L∞-gains. Robust stability analysis is performed using Integral Linear Constraints (ILCs) for which several class es of uncertainties are discussed. The approach is then extended to robust stabilization and performance optimiza tion. The obtained results are expressed in terms of robust linear programming problems that are equivalently turned i nto finite dimensional ones using Handelman’s Theorem. Several examples are provided for illustration.

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