Actas de congresos
A Formulation Of Lmi For Analysis Of Establishing With Lyapunov Functions Of Lur'e-persidskii Type [uma Formulação Lmi Para A Análise De Estabilidade Com Funções De Lyapunov Do Tipo Lur'e-persidskii]
Registro en:
Controle Y Automacao. , v. 13, n. 1, p. 25 - 33, 2002.
1031759
2-s2.0-18844477912
Autor
De Oliveira M.C.
Hsu L.
Geromel J.C.
Institución
Resumen
In this paper we propose an unified construction of Lyapunov functions based on Lur'e type functions that allows us to go from Persidskii's to pure quadratic functions. Such Lyapunov functions allows the establishment of the absolute stability of nonlinear systems with nonlinearities belonging to given sectors. The sectors can be finite or infinite. An stability criterion is formulated in terms of Linear Matrix Inequalities (LMI). The parameters that define the sectors are present in the given LMI and are made available for optimization, leading to several optimization problems that are able, to determine the available robustness levels for several sector configurations. 13 1 25 33 Albertini, F., D'Alessandro, D., Asymptotic stability of continuous-time systems with saturation nonlinearities (1996) Systems & Control Letters, 29 (3), pp. 175-180 Boyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAM, Philadelphia, PA Chu, Y.-C., Glover, K., Bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities (1999) IEEE Transactions on Automatic Control, 44 (3), pp. 471-483 Colaneri, P., Geromel, J.C., Locatelli, A., (1997) Control Theory and Design: An RH2- RH∞ viewpoint, , Academic Press, San Diego, CA De Oliveira, M.C., Geromel, J.C., Hsu, L., A new absolute stability test for systems with state-dependent perturbations (2002) International Journal of Robust and Nonlinear Control Geromel, J.C., De Oliveira, M.C., Hsu, L., LMI characterization of structural and robust stability (1998) Linear Algebra and Its Applications, 285 (1-3), pp. 69-80 Haddad, W.M., Bernstein, D.S., Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. Part I: Continuous-time theory (1993) International Journal of Robust and Nonlinear Control, 3 (4), pp. 313-339 Hsu, L., Salgado, L.A., Structural properties in the stability problem of interconnected systems (1980) Proceedings of the 2nd IFAC Symposium on Large Scale Systems, pp. 67-77 Kaszkurewicz, E., Bhaya, A., Robust stability and diagonal Lyapunov functions (1993) SIAM Journal on Matrix Analysis and Applications, 14, pp. 508-520 Kaszkurewicz, E., Bhaya, A., On a class of globally stable neural circuits (1994) IEEE Transactions on Circuits and Systems - I: Fundamental theory and applications, 41 (2), pp. 171-174 Kaszkurewicz, E., Hsu, L., Stability of nonlinear systems: A structural approach (1979) Automatica, 15, pp. 609-614 Khalil, H.K., (1996) Nonlinear Systems, second edn, , Prentice Hall, Inc, Englewood Cliffs, NJ Nesterov, Y.E., Nemirovskii, A., (1994) Interior Point Polynomial Methods in Convex Programming, , SIAM, Philadelphia, PA Pai, M.A., (1981) Power systems stability, , Elsevier, Amsterdam, The Netherlands Persidskii, S.K., Problem on absolute stability (1969) Automation and Remote Control, 12, pp. 1889-1895 Thygesen, U.H., Skelton, R.E., Linear systems with finite signal-to-noise ratio: A robustness approach (1995) Proceedings of the 34th IEEE Conference on Decision and Control, pp. 4157-4162