Robustness analysis and synthesis for nonlinear uncertain systems

Wei-Min Lu, J.C. Doyle
1997 IEEE Transactions on Automatic Control  
A state-space characterization of robustness analysis and synthesis for nonlinear uncertain systems is proposed. The robustness of a class of 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 in the linear case, scalings are used to find a Lyapunov or storage function that give sufficient conditions for robust stability and performances. Sufficient conditions for the
more » ... 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 synthesis is not more difficult than that for checking Lyapunov stability; the numerical solutions for robustness problems are approximated by the use of finite element methods or finite difference schemes, and the computations are reduced to solving linear matrix inequalities. Unfortunately, while the development in this paper parallels the corresponding linear theory, the resulting computational consequences are, of course, not as favorable. Index Terms-Computational nonlinear control, nonlinear control systems, nonlinear matrix inequality (NLMI), robust control, robust performance, state space.
doi:10.1109/9.650015 fatcat:6do7gyglprgrhgxqkylew5hlbq