Constrained Nonlinear Polynomial Time-Delay Systems: A Sum-of-Squares Approach to Estimate the Domain of Attraction

• Published in: IEEE transactions on automatic control Vol. 57; no. 10; pp. 2673 - 2679
• Main Authors: Franze, G., Famularo, D., Casavola, A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.10.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Approximation methods; Asymptotic stability; Attraction; Automatic control; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control systems; Control theory. Systems; Delay; Design engineering; Direction of arrival estimation; Domain of attraction (DoA); Estimates; Exact sciences and technology; Nonlinearity; Optimization; Polynomials; Programming; Stability analysis; sum-of-squares (SOS); System theory; Domain of attraction (DoA); Non linear control; Control synthesis; Semi definite programming; Delay system; Quadratic programming; Non linear system; Geometric programming; Polynomial time; Minimum time; sum-of-squares (SOS); Quadratic cost; Domain of attraction; Lyapunov function
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2012.2190189

A sum-of-squares (SOS) approach is proposed to estimate the domain of attraction (DoA) of regulated nonlinear polynomial time-delay systems subject to input constraints. It will be shown that the joint use of semialgebraic geometric arguments and semidefinite programming methods provides an efficient tool for Lyapunov-based control system analysis and design for this class of nonlinear delayed systems. Specifically, a two-step procedure is presented which consists of deriving first a Lyapunov-Krasovskii functional/controller pair complying with the prescribed constraints and computing then an estimate of the DoA.