ROBUSTNESS ANALYSIS AND SYNTHESIS FOR NONLINEAR UNCERTAIN SYSTEMS

A state-space characterization of robustness analysis and synthesis fo r nonlinear uncertain systems is proposed, The robustness of a class o f nonlinear systems subject to L-2-bounded structured uncertainties is characterized in terms of a nonlinear matrix inequality (NLMI), which yields a convex feasibility problem, As ire the linear case, scalings are used to find a Lyapunov or storage function that give sufficient conditions for robust stability and performances, Sufficient condition s for the solvability of robustness synthesis problems are represented in terms of NLMI's as well, With the proposed NLMI characterizations, it is shown that the computation needed for robustness analysis and s ynthesis is not more difficult than that for checking Lyapunov stabili ty; the numerical solutions for robustness problems are approximated b y the use of finite element methods or finite difference schemes, and the computations are reduced to solving linear matrix inequalities. Un fortunately, while the development in this paper parallels the corresp onding linear theory, the resulting computational consequences are, of course, not as favorable.