Robust stability and stabilization of uncertain linear positive systems via Integral Linear Constraints: L1- and Linfinity-gains characterization
For control theorists and engineers working with positive systems, this provides a new method to handle uncertainties using linear programming, but the approach is incremental as it extends existing dissipativity and Lyapunov methods.
The paper develops a framework for robust stability and stabilization of uncertain linear positive systems using copositive linear Lyapunov functions and dissipativity theory with linear supply-rates, characterizing L1- and Linfinity-gains. The results are expressed as robust linear programs solved via Handelman's Theorem, with examples provided.
Copositive linear Lyapunov functions are used along with dissipativity 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 L1- and Linfinity-gains. Robust stability analysis is performed using Integral Linear Constraints (ILCs) for which several classes of uncertainties are discussed. The approach is then extended to robust stabilization and performance optimization. The obtained results are expressed in terms of robust linear programming problems that are equivalently turned into finite dimensional ones using Handelman's Theorem. Several examples are provided for illustration.