Title :
Contractive polyhedra for linear continuous-time systems with saturating controls
Author :
Da Silva, J. M Gomes, Jr. ; Tarbouriech, S.
Author_Institution :
Dept. of Electr. Eng., Univ. Federal do Rio Grande do Sul, Porto Alegre, Brazil
Abstract :
The study of the contractivity properties of polyhedral sets with respect to (w.r.t) linear systems subject to control saturation is addressed. The analysis of the nonlinear behavior of the closed-loop saturated system is made by dividing the state space in regions of saturation. In each one of these regions, the system evolution can be represented by one of a linear system with an additive disturbance. From this representation, a necessary and sufficient algebraic condition for the contractivity of a polyhedral set w.r.t the control saturating system is stated. Consequently, a Lyapunov function can be associated with the polyhedral set and the local asymptotic stability of the closed-loop system inside the set is guaranteed. The conditions for polyhedral contractivity are used to state an algorithm, based on linear programming, to compute polyhedral regions of local asymptotic stability for the closed-loop saturated system
Keywords :
asymptotic stability; closed loop systems; continuous time systems; control nonlinearities; linear programming; linear systems; state-space methods; Lyapunov function; additive disturbance; closed-loop saturated system; contractive polyhedra; contractivity properties; control saturation; linear continuous-time systems; local asymptotic stability; necessary and sufficient algebraic condition; nonlinear behavior; polyhedral regions; polyhedral set; saturating controls; system evolution; Asymptotic stability; Control systems; Ear; Linear programming; Linear systems; Nonlinear control systems; Open loop systems; State feedback; State-space methods; Vectors;
Conference_Titel :
American Control Conference, 1999. Proceedings of the 1999
Conference_Location :
San Diego, CA
Print_ISBN :
0-7803-4990-3
DOI :
10.1109/ACC.1999.786227
