Title :
Stability region analysis using sum of squares programming
Author :
Tan, Weehong ; Packard, Andrew
Author_Institution :
Dept. of Mech. Eng., California Univ., Berkeley, CA
Abstract :
We propose using (bilinear) sum of squares programming for enlarging a provable region of attraction of polynomial systems using polynomial Lyapunov functions. In order to keep the number of decision variables low, we propose the use of composite Lyapunov functions. We also present a method of finding outer bounds of attractive invariant sets for polynomial systems. Excellent results for some examples were obtained using the proposed methods and the PENBMI solver
Keywords :
Lyapunov methods; mathematical programming; nonlinear systems; polynomials; stability; PENBMI solver; attractive invariant sets; bilinear sum of squares programming; composite Lyapunov functions; decision variables; nonlinear systems; polynomial Lyapunov functions; polynomial systems; stability region analysis; Aircraft; Ellipsoids; Functional programming; Level set; Lyapunov method; Mechanical factors; Nonlinear systems; Polynomials; Power system stability; Stability analysis;
Conference_Titel :
American Control Conference, 2006
Conference_Location :
Minneapolis, MN
Print_ISBN :
1-4244-0209-3
Electronic_ISBN :
1-4244-0209-3
DOI :
10.1109/ACC.2006.1656562
