Robust stability: perturbed systems with perturbed equilibria
Systems & Control Letters
Robust and optimal control
On contraction analysis for non-linear systems
Automatica (Journal of IFAC)
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Linearized analysis versus optimization-based nonlinear analysis for nonlinear systems
ACC'09 Proceedings of the 2009 conference on American Control Conference
Verification of annotated models from executions
Proceedings of the Eleventh ACM International Conference on Embedded Software
| Hi-index | 22.14 |
A wide variety of stability and performance questions about linear dynamical systems can be reformulated as convex optimization problems involving linear matrix inequalities (LMIs). These techniques have been recently extended to nonlinear systems with polynomial or rational dynamics through the use of sum of squares (SOS) programming. In this paper we further extend the class of systems that can be analyzed with convexity-based methods. We show how to analyze the robust stability properties of uncertain nonlinear systems with polynomial or rational dynamics, via contraction analysis and SOS programming. Since the existence of a global contraction metric is a sufficient condition for global stability of an autonomous system, we develop an algorithm for finding such contraction metrics using SOS programming. The search process is made computationally tractable by relaxing matrix definiteness constraints, the feasibility of which indicates the existence of a contraction metric, to SOS constraints on polynomial matrices. We illustrate our results through examples from the literature and show how our contraction-based approach offers advantages when compared with traditional Lyapunov analysis.