Title :
Existence of parameter-dependent Lyapunov functions assuring robust stability via SOS
Author :
Lo, Ji-Chang ; Tsai, Chin-Fu
Author_Institution :
Mech. Eng., Nat. Central Univ., Jhongli, Taiwan
Abstract :
An SOS relaxation technique seeking homogeneous polynomially parameter dependent (HPPD) Lyapunov function to non-quadratic stability is proposed. We investigate non-quadratic relaxed conditions characterized by sum of squares, exploiting the algebraic property of Polya Theorem to construct a family of finite-dimensional SOS relaxations that releases conservatism without adding any slack matrices. Lastly, numerical experiments to illustrate the advantage of the relaxation, being simple and effective, are provided.
Keywords :
Lyapunov methods; matrix algebra; multidimensional systems; relaxation theory; robust control; HPPD Lyapunov function; Polya theorem; SOS relaxation technique; algebraic property; finite-dimensional SOS relaxations; homogeneous polynomially parameter dependent Lyapunov function; nonquadratic relaxed conditions; nonquadratic stability; parameter-dependent Lyapunov functions; robust stability; slack matrices; sum of squares; Eigenvalues and eigenfunctions; Linear matrix inequalities; Lyapunov methods; Polynomials; Stability analysis; Symmetric matrices; Uncertain systems; Homogeneous polynomials; Linear matrix inequality; Non-common P; Parameter-dependent LMIs (PD-LMIs); Relaxation;
Conference_Titel :
Control Conference (ASCC), 2011 8th Asian
Conference_Location :
Kaohsiung
Print_ISBN :
978-1-61284-487-9
Electronic_ISBN :
978-89-956056-4-6
