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]
Controle Y Automacao. , v. 13, n. 1, p. 42 - 50, 2002.
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.1314250Bazaraa, M.S., Jarvis, J.J., Sherali, H.D., (1990) Linear Programming and Network Flows, , Wiley, New York NYBitsoris, G., Gravalou, E., Comparison principle, positive invariance and constrained regulation of nonlinear systems (1995) Automatica, 31 (2), pp. 217-222Blanchini, F., Set invariance in control: A survey (1999) Automatica, 35 (11), pp. 1747-1768Dórea, 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. 521-542Hennet, 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 IMangasarian, O.L., (1974) Nonlinear Programming, , SIAM, Philadelphia PAMilani, 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, USAMilham, C.B., Fast feasibility methods for linear programming (1976) OPSEARCH, 13 (3-4), pp. 198-204Romanchuck, B.G., Computing regions of attractions with polytopes: Planar case (1996) Automatica, 32 (12), pp. 1727-1732Silva 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. 2081-2085Slotine, J.E., Li, W., (1981) Applied Nonlinear Control, , Prentice-Hall, Englewood Cliffs NJTarbouriech, 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