Actas de congresos
Linear Lyapunov Function For Parts Before Linear Systems With Saturated Controls [funções De Lyapunov Lineares Por Partes Para Sistemas Lineares Com Controles Saturáveis]
Registro en:
Controle Y Automacao. , v. 13, n. 1, p. 42 - 50, 2002.
1031759
2-s2.0-0036308212
Autor
Milani B.E.A.
Coelho A.D.
Institución
Resumen
This paper is concerned with piecewise-linear functions as Lyapunov function candidates for stability analysis of time-invariant discrete-time linear systems with saturating closed-loop control inputs. New necessary and sufficient conditions for positive definite piecewise-linear functions be Lyapunov functions are presented. A computational procedure is proposed for determination of such Lyapunov functions and associated polyhedral regions of local asymptotic stability. Compared to Minkowski functions, piecewise-linear functions present strictly better performance, being naturally more flexible and better adapted to the radially variable dynamic behavior of saturated systems. 13 1 42 50 Bazaraa, M.S., Jarvis, J.J., Sherali, H.D., (1990) Linear Programming and Network Flows, , Wiley, New York NY Bitsoris, G., Gravalou, E., Comparison principle, positive invariance and constrained regulation of nonlinear systems (1995) Automatica, 31 (2), pp. 217-222 Blanchini, F., Set invariance in control: A survey (1999) Automatica, 35 (11), pp. 1747-1768 Dórea, C.E.T., Hennet, J.C., (A,B) - Invariant polyhedral sets of linear discrete-time systems (1999) Journal of Optimization Theory and Applications, 103 (3), pp. 521-542 Hennet, J.C., Une extension du lemme de farkas et son application au problème de regulation linéaire sous contraintes (1989) C.R. Acad. Sci. Paris, 308, pp. 415-419. , Série I Mangasarian, O.L., (1974) Nonlinear Programming, , SIAM, Philadelphia PA Milani, B.E.A., Contractive polyhedra for discrete-time linear systems with saturating controls (1999) Proceedings of the 38th Conference on Decision and Control, , Phoenix AZ, USA Milham, C.B., Fast feasibility methods for linear programming (1976) OPSEARCH, 13 (3-4), pp. 198-204 Romanchuck, B.G., Computing regions of attractions with polytopes: Planar case (1996) Automatica, 32 (12), pp. 1727-1732 Silva J.M.G., Jr., Tarbouriech, S., Polyhedral regions of local asymptotic stability for discrete-time linear systems with saturating controls (1999) IEEE Transactions on Automatic Control, 44 (11), pp. 2081-2085 Slotine, J.E., Li, W., (1981) Applied Nonlinear Control, , Prentice-Hall, Englewood Cliffs NJ Tarbouriech, S., Silva J.M.G., Jr., Admissible polyhedra for discrete-time linear systems with saturating controls (1997) Proceedings of 1997 American Control Conference, , Albuquerque NM, USA