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On state feedback stabilization of singular systems with random abrupt changes. (English) Zbl 1144.93029
Summary: This paper deals with the class of continuous-time singular linear systems with random abrupt changes. The state feedback stabilization and its robustness for this class of systems with norm-bounded uncertainties are tackled. Sufficient conditions for designing either a stabilizing controller or a robust stabilizing controller are developed in the LMI setting. The developed sufficient conditions are used to synthesize the state feedback controller that guarantees that either the nominal system or the uncertain system is piecewise regular, impulse free and stochastically stable or robust stochastically stable.

MSC:
93E15 Stochastic stability in control theory
93D10 Popov-type stability of feedback systems
93B50 Synthesis problems
93B52 Feedback control
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[1] Boukas, E.K., Liu, Z.K.: Deterministic and Stochastic Systems with Time-Delay. Birkhauser, Boston (2002) · Zbl 1056.93001
[2] Mariton, M.: Control of nonlinear systems with Markovian parameter changes. IEEE Trans. Automat. Contr. 36, 233–238 (1991) · Zbl 0764.93084 · doi:10.1109/9.67303
[3] Boukas, E.K., Hang, H.: Exponential stability of stochastic systems with Markovian jumping parameters. Automatica 35, 1437–1441 (1999) · Zbl 0932.93084 · doi:10.1016/S0005-1098(99)00033-3
[4] Boukas, E.K., Liu, Z.K.: Robust stability and stability of Markov jump linear uncertain systems with mode-dependent time delays. J. Optim. Theory Appl. 209, 587–600 (2001) · Zbl 0988.93062 · doi:10.1023/A:1017515721760
[5] Feng, X., Loparo, K.A., Ji, Y., Chizeck, H.J.: Stochastic stability properties of jump linear systems. IEEE Trans. Automat. Contr. 37, 38–53 (1992) · Zbl 0747.93079 · doi:10.1109/9.109637
[6] Ji, Y., Chizeck, H.J.: Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control. IEEE Trans. Automat. Contr. 35, 777–788 (1990) · Zbl 0714.93060 · doi:10.1109/9.57016
[7] Mao, X.: Stability of stochastic differential equations with Markovian switching. Stoch. Process. Their Appl. 79, 45–67 (1999) · Zbl 0962.60043 · doi:10.1016/S0304-4149(98)00070-2
[8] De Souza, C.E., Fragoso, M.D.: Robust H filtering for Markovian jump linear systems. In: Proceedings of the 35th IEEE Conference on Decision and Control Kobe, Japan, pp. 4808–4813 (1996)
[9] Shi, P., Boukas, E.K.: H control for Markovian jumping linear systems with parametric uncertainty. J. Optim. Theory Appl. 95, 75–99 (1997) · Zbl 1026.93504 · doi:10.1023/A:1022683311870
[10] Cao, Y.Y., Lam, J.: Robust H control of uncertain Markovian jump systems with time delay. IEEE Trans. Automat. Contr. 45(1), 77–83 (2000) · Zbl 0983.93075 · doi:10.1109/9.827358
[11] Boukas, E.K., Liu, Z.K.: Robust H control of discrete-time Markovian jump linear systems with mode-dependent time delays. IEEE Trans. Automat. Contr. 46, 1918–1924 (2001) · Zbl 1005.93050 · doi:10.1109/9.975476
[12] Boukas, E.K., Liu, Z.K., Liu, G.X.: Delay-dependent robust stability and H control of jump linear systems with time delay. Int. J. Contr. 74, 329–340 (2001) · Zbl 1015.93069 · doi:10.1080/00207170010008752
[13] Dai, L.: Singular Control Systems. Lecture Notes in Control and Information Sciences, vol. 118. Springer, New York (1989) · Zbl 0669.93034
[14] Kumar, A., Daoutidis, P.: Feedback control of nonlinear differential-algebraic equation systems. AIChE J. 41, 619–636 (1995) · doi:10.1002/aic.690410319
[15] Lewis, F.L.: A survey of linear singular systems. Circuits Syst. Signal Process. 5, 3–36 (1986) · Zbl 0613.93029 · doi:10.1007/BF01600184
[16] Newcomb, R.W.: The semistate description of nonlinear time-variable circuits. IEEE Trans. Circuits Syst. 28, 62–71 (1981) · doi:10.1109/TCS.1981.1084908
[17] Fridman, E.: A Lyapunov-based approach to stability of descriptor systems with delay. In: Proceedings of the 40th IEEE Conference on Control and Decision, Orlando, Florida, pp. 2850–2855 (2001)
[18] Lan, W., Huang, J.: Semiglobal stabilization and output regulation of singular linear systems with input saturation. IEEE Trans. Automat. Contr. 48, 1274–1280 (2003) · Zbl 1364.93644 · doi:10.1109/TAC.2003.814276
[19] Xu, S., Dooren, P.V., Stefan, R., Lam, J.: Robust stability and stabilization of discrete-time singular systems with state delay and parameter uncertainty. IEEE Trans. Automat. Contr. 47, 1122–1128 (2002) · Zbl 1364.93723 · doi:10.1109/TAC.2002.800651
[20] Xu, S., Lam, J.: Robust stability and stabilization of discrete-time singular systems: an equivalent characterization. IEEE Trans. Automat. Contr. 49, 568–574 (2004) · Zbl 1365.93375 · doi:10.1109/TAC.2003.822854
[21] Xu, S., Yang, C.: Stabilization of discrete-time singular systems: a matrix inequalities approach. Automatica 35, 1613–1617 (1999) · Zbl 0959.93048 · doi:10.1016/S0005-1098(99)00061-8
[22] Fletcher, L.R.: Assignment and controllability subspaces in descriptor systems. Int. J. Contr. 66, 677–709 (1997) · Zbl 0876.93040 · doi:10.1080/002071797224504
[23] Takaba, K., Morihira, N., Katayama, T.: A generalized Lyapunov theorem for descriptor systems. Syst. Control Lett. 24, 49–51 (1995) · Zbl 0883.93035 · doi:10.1016/0167-6911(94)00041-S
[24] Verghese, G.C., Levy, B.C., Kailath, T.: A generalized state-space for singular systems. IEEE Trans. Automat. Contr. 26, 811–831 (1981) · Zbl 0541.34040 · doi:10.1109/TAC.1981.1102763
[25] Xu, S., Lam, J., Zhang, L.: Robust D-stability analysis for uncertain discrete singular systems with state delay. IEEE Trans. Circuits Syst. I. 49, 551–555 (2002) · Zbl 1368.93513 · doi:10.1109/81.995677
[26] Xu, S., Lam, J.: Robust stability for uncertain discrete singular systems with state delay. Asian J. Control 5, 399–405 (2003) · doi:10.1111/j.1934-6093.2003.tb00132.x
[27] Boukas, E.K., Liu, Z.K.: Delay-dependent stability analysis of singular linear continuous-time systems. IEE Proc. Control Theory Appl. 150(2), 325–330 (2003) · doi:10.1049/ip-cta:20030635
[28] Boukas, E.K., Liu, Z.K.: Delay-dependent stabilization of singularly perturbed jump linear systems. Int. J. Contr. 77(3), 310–319 (2004) · Zbl 1070.93037 · doi:10.1080/00207170310001657298
[29] Shi, P., Boukas, E.K.: On H control design for singular continuous-time delay systems with parametric uncertainties. Nonlinear Dyn. Syst. Theory 4(1), 59–71 (2004) · Zbl 1073.93020
[30] Boukas, E.K.: Stochastic Switching Systems: Analysis and Design. Birkhauser, Boston (2005) · Zbl 1108.93074
[31] Boukas, E.K.: On robust stability of singular systems with random abrupt changes. Int. J. Hybrid. Syst. (2005) · Zbl 1089.34046
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