Artículos de revistas
Continuous-time State-feedback H 2-control Of Markovian Jump Linear Systems Via Convex Analysis
Registro en:
Automatica. , v. 35, n. 2, p. 259 - 268, 1999.
51098
2-s2.0-0033077957
Autor
Costa O.L.V.
Do Val J.B.R.
Geromel J.C.
Institución
Resumen
Continuous-time H 2-control problem for the class of linear systems with Markovian jumps (MJLS) using convex analysis is considered in this paper. The definition of the H 2-norm for continuous-time MJLS is presented and related to the appropriate observability and controllability Gramians. A convex programming formulation for the H 2-control problem of MJLS is developed. That enables us to tackle the optimization problem of MJLS under the assumption that the transition rate matrix Π = [π ij] for the Markov chain may not be exactly known, but belongs to an appropriate convex set. An equivalence between the convex formulation when Π is exactly known and the usual dynamic programming approach of quadratic optimal control of MJLS is established. It is shown that there exists a solution for the convex programming problem if and only if there exists the mean-square stabilizing solution for a set of coupled algebraic Riccati equations. These results are compared with other related works in the current literature. © 1999 Elsevier Science Ltd. All rights reserved. 35 2 259 268 Abou-Khandil, H., Freiling, G., Jank, G., Solution and asymptotic behavior of coupled Riccati equations in jump linear systems (1994) IEEE Trans. on Automat. Control, 39, pp. 1631-1636 Blair Jr., W.P., Sworder, D.D., Continuous-time regulation of a class of econometric models (1975) IEEE Trans. Systems Man Cybernet, 5, pp. 341-346 Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities and Control Theory, , Philadelphia: SIAM El Ghaoui, E., Nikoukhah, R., Delebecque, F., (1995) LMITOOL: A Front-end for LMI Optimization -User's Guide, , ftp.ensa.fr/pub/elghaoui/lmitool Costa, O.L.V., Do Val, J.B.R., Geromel, J.C., A convex programming approach to H 2-control of discrete-time Markovian jump linear systems (1997) Int. J. Control, 66, pp. 557-579 Gajic, Z., Borno, I., Lyapunov iterations for optimal control of jump linear systems at steady state (1995) IEEE Trans. Automat. Control, 40, pp. 1971-1975 Feng, X., Loparo, K.A., Ji, Y., Chizeck, H.J., Stochastic stability properties of jump linear systems (1992) IEEE Trans. Automat. Control, 37, pp. 38-53 Ji, Y., Chizeck, H.J., Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control (1990) IEEE Trans. Automat. Control, 35, pp. 777-788 Mariton, M., Almost sure and moments stability of jump linear systems (1988) Systems and Control Lett., 11, pp. 393-397 Mariton, M., (1990) Jump Linear Systems in Automatic Control, , New York: Marcel Dekker Rami, M.A., El Ghaoui, E., Robust state-feedback stabilization of jump linear systems via LMIs (1996) Int. J. Robust Nonlinear Control, 6, pp. 1015-1022 Rami, M.A., El Ghaoui, E., LMI optimization for nonstandard Riccati equations arising in stochastic control (1996) IEEE Trans. Automat. Control, 41, pp. 1666-1671 Vandenberghe, L., Boyd, S., (1994) Software for Semidefinite Programming -User's Guide, , isl.stanford.edu/pub/boyd/semidef_prog