On the stability of one dimensional discrete-time jump linear systems

• Autorzy: Czornik, A. , Nawrat, A. , Rabsztyn, S.
• Języki publikacji: EN

Abstrakty

EN

In this paper we present necessary and sufficient conditions for "delta" - moment stability and almost sure stability of one-dimensional discrete-time linear systems subject is equivalent to "delta"-moment stability for certain "delta">0.

Słowa kluczowe

EN

jump linear systems; almost sure stability; moment stability

• Czasopismo: Archives of Control Sciences
• Rocznik: 2003
• Tom: Vol. 13, no. 1
• Strony: 81-93
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Czornik, A.

• Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

autor

Nawrat, A.

• Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

autor

Rabsztyn, S.

• Department of Mathematics, Silesian University of Technology, Kasubska 23, 44-100 Gliwice, Poland

Bibliografia

• [1] R. Akella and P. R. Kumar: Optimal control of production rate in failure prone manufacturing systems. IEEE Trans, Automatic Control, 31 (1086), 116-126.
• [2] L. Arnold: A formula connecting sample and moment stability of linear stochastic systems. SIAM J. Applied Mathematic. 44( 3), (1984), 793-802.
• [3] J. D. Birdwel: On reliable control systems design. Ph. D. Dissertation. Electrical Systems Lab., Mass. Inst. Technology, report no. ESL-TII-821, 1978.
• [4] M. D. Costa and M. D. Fragoso: Stability results for discrete-time linear systems with Markovian jumping parameters. J. Mathematical Analysis and Applications, 179(1), (1993), 154-178.
• [5] K. H. Du and T. V. Nhung: Relations between the sample and moment Lyapunov exponents. Stochastics and Stochastic Reports. 37 (1991), 201-211.
• [6] Y. Fang: Stability analysis of linear control systems with uncertain parameters. Ph.D. dissertation. Department of Systems. Control and Industrial Engineering. Case Western Reserve University, Cleveland, Ohio, 1994.
• [7] Y. Fang, K. A. Loparo and X. Feng: Almost sure and –beta-moment stability of jump linear systems. Int. J. Control, 59(5), (1994), 1281-1307.
• [8] Y. Fang: A new general sufficient condition for almost sure stability of jump linear systems. IEEE Trans. Automatic Control, 42(3), (1997), 378-382.
• [9] X. Feng K. A. Loparo, Y. Ji and H. J. Chizeck: Stochastic stability properties of jump linear systems. IEEE Trans. Automatic Control, 37(1), (1992), 38-53.
• [10] D. Freedman: Markov Chains. Springer-Verlag. New York, 1983.
• [11] R. A. Horn and C. R. Johnson: Matrix. Analysis. Cambridge University Press. 1985.
• [12] Y. Ji. H. J. Chizeck. X. Feng and K. A. Loparo: Stability and Control of Discrete-Time Jump Linear Systems. Control Theory and Advanced Technology. (1991), 247-270.
• [13] T. Kazangey and D. D. Sworder: Effective federal polices for regulating residential housing. Proc. Summer Comp. Simulation Conf., Los Angeles, (1971), 1120-1128.
• [14] A. Leizarowitz: Estimates and exect expressions for Lyapunov exponents of stochastic linear differential equations. Stochastics, 24 (1988), 335-356.
• [15] Z.G. Li, Y. C. Soh and C.Y. Wen: Sufficient conditions for Almost sure stability of jump linear systems. IEEE Trans. Automatic Control, 45 (2000), 1325-1329.
• [16] M. Mariton: Jump Linear Systems in Automatic Control. Marcel Dekker. New York and Besel. 1990.
• [17] R. C. Montgomery: Reliability considerations in placement of control systems components. Proc. AIAA Guidance and Control Conference. Gatlinburg, (1983), 571-574.
• [18] D. D. Siljak: Reliable control using multiple control systems. J. Control, 31(2), (1980), 303-329.
• [19] D. D. Sworder and R. O. Rogers: An LQ- solution to a control problem associated with solar thermal central receiver. IEEE Trans. Automatic Control, 28 (1983), 971-978.
• [20] A. S. Willsky and B. C. Levy: Stochastic stability research for complex power systems. Lab. Inf. Decision Systems. Mass. Inst. Technology, report no. ET-76-C-01-2295, 1979.