Ultimate Boundedness Sets For Continuous-time Linear Systems With Deadzone Feedback Controls

This paper is concerned with the construction of positively invariant convex polyhedral uniform ultimate boundedness sets for linear continuous-time systems with stabilizing deadzone feedback control laws. The objective is delimitation and region of attraction estimation of possible limit cycles around origin of open-loop unstable systems. Limit cycle delimitation is performed via construction of a positively invariant convex compact polyhedral estimate of the minimal positively invariant set containing an arbitrarily small neighborhood of origin. Region of attraction estimation is performed via construction of a piecewise-affine Lyapunov function assuring uniform ultimate boundedness in the above mentioned convex positively invariant polyhedral set. © 2005 IEEE.200568536858Slotine, J.E., Li, W., (1981) Applied Nonlinear Control, , Prentice-Hall, Englewood Cliffs, NJ;Zames, G., Falb, P.L., Stability Conditions for Systems with Monotone and Slope-restricted Nonlinearities (1968) SIAM Journal of Control, 6 (1), pp. 89-108Khalil, H.K., (1992) Nonlinear Systems, , Macmillan, New York;Jönsson, U., Stability Criterion for Systems with Neutrally Stable Modes and Deadzone Nonlinearities CALTECH Report, , CDS97-007, 1997La Salle, J.P., (1976) The Stability of Dynamical Systems, , SIAM, Philadelphia;Milani, B.E.A., Coelho, A.D., Ultimate Boundedness Sets for Discrete-time Linear Systems with Deadzone Feedback Controls (2001) 40th IEEE Conference on Decision and Control, pp. 2163-2164. , Orlando, FLRouche, N., Habets, P., Laloy, M., (1997) Stability Theory by Lyapunov's Direct Method, , Springer Verlag, New York, NY;Bartle, R.G., Sherbert, D.R., (1982) Introduction to Real Analysis, , John Wiley & Sons Inc, New York, NY;Blanchini, F., Set Invariance in Control: A Survey (1999) Automatica, 35, pp. 1747-1746Mangasarian, O.L., (1994) Nonlinear Programming, , SIAM, Philadelphia, PA;Milani, B.E.A., Piecewise-affine Lyapunov Functions for Discrete-time Linear Systems with Saturating Controls (2002) Automatica, 38 (12), pp. 2177-218