Generalized practical stability analysis of discontinuous dynamical systems

• Autorzy: Zhai G. , Michel A. N.
• Języki publikacji: EN

Abstrakty

EN

In practice, one is not only interested in the qualitative characterizations provided by the Lyapunov stability, but also in quantitative information concerning the system behavior, including estimates of trajectory bounds, possibly over finite time intervals. This type of information has been ascertained in the past in a systematic manner using the concept of practical stability. In the present paper, we give a new definition of generalized practical stability (abbreviated as GP-stability) and establish some sufficient conditions concerning GP-stability for a wide class of discontinuous dynamical systems. As in the classical Lyapunov theory, our results constitute a Direct Method, making use of auxiliary scalar-valued Lyapunov-like functions. These functions, however, have properties that differ significantly from the usual Lyapunov functions. We demonstrate the applicability of our results by means of several specific examples.

Słowa kluczowe

EN

discontinuous dynamical system; quantitative analysis; generalized practical stability; Lyapunov-like function

PL

układ dynamiczny nieciągły; analiza ilościowa; funkcja Lyapunova

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2004
• Tom: Vol. 14, no 1
• Strony: 5--12
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Zhai G.

• Department of Opto-Mechatronics, Wakayama University, 930 Sakaedani, Wakayama 640-8510, Japan

autor

Michel A. N.

• Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA

Bibliografia

• [1] DeCarlo R., Branicky M., Pettersson S. and Lennartson B. (2000): Perspectives and results on the stability and stabilizability of hybrid systems. — Proc. IEEE, Vol. 88, No. 7, pp. 1069–1082.
• [2] Hespanha J.P. and Morse A.S. (1999): Stability of switched systems with average dwell-time. — Proc. 38th IEEE Conf. Decision and Control, Phoenix, pp. 2655–2660.
• [3] Michel A.N. (1999): Recent trends in the stability analysis of hybrid dynamical systems. — IEEE Trans. Circ. Syst.-I: Fund. Theory Applic., Vol. 45, No. 1, pp. 120–134.
• [4] Michel A.N. (1970): Quantitative analysis of simple and interconnected systems: Stability, boundedness and trajectory behavior. — IEEE Trans. Circ. Theory, Vol. 17, No. 3, pp. 292–301.
• [5] Michel A.N. and Porter D.W. (1971): Analysis of discontinuous large-scale systems: Stability, transient behaviour and trajectory bounds. — Int. J. Syst. Sci., Vol. 2, No. 1, pp. 77–95.
• [6] Michel A.N., Wang K. and Hu B. (2000): Qualitative Theory of Dynamical Systems, 2nd Ed.. — New York: Marcel Dekker.
• [7] Lakshmikantham V., Leela S. and Martynyuk A.A. (1991): Practical Stability of Nonlinear Systems. — Singapore: World Scientific.
• [8] Weiss L. and Infante E.F. (1967): Finite time stability under perturbing forces and on product spaces. — IEEE Trans. Automat. Contr., Vol. AC–12, No. 1, pp. 54–59.
• [9] Zhai G. and Michel A.N. (2002): On practical stability of switched systems. — Proc. 41st IEEE Conf. Decision and Control, Las Vegas, pp. 3488–3493.
• [10] Zhai G., Hu B., Yasuda K. and Michel A.N. (2000): Piecewise Lyapunov functions for switched systems with average dwell time.—Asian J. Contr., Vol. 2, No. 3, pp. 192–197.
• [11] Zhai G., Hu B., Yasuda K. and Michel A.N. (2001): Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach. — Int. J. Syst. Sci., Vol. 32, No. 8, pp. 1055–1061.
• [12] Zhai G., Hu B., Yasuda K. and Michel A.N. (2002): Stability and L2 gain analysis of discrete-time switched systems.— Trans. Inst. Syst. Contr. Inf. Eng., Vol. 15, No. 3, pp. 117–125.