Abstract
This paper presents a hybrid model suitable for analysis of hybrid systems and for synthesis of hybrid controllers, and the linear hybrid system which combines continuous linear dynamics in each discrete state with discrete dynamics having the Markov property. The stochastic stability of the linear hybrid system is defined and the stability condition and the stabilizability condition is proposed. A simple example is given to illustrate the proposed framework.
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References
K.J. Astrom and B. Wittenmark(1989), Adaptive Control, USA: Addison-Wesley Pub. Co.
A.Benveniste and P. Le Guernic(1990), Hybrid Dynamical Systems Theory and the SIGNAL Language, IEEE Trans. Automat. Contr., Vol. 35, No. 5, pp.535–546.
M.S. Branicky(1993), Topology of Hybrid Systems, Proc. of the 32th Conf. Decision and Control, pp.2309–2314.
C.M. Özveren and A.S. Willsky(1991), Stability and Stabilizability of Discrete Event Dynamic, J. of ACM, vol. 38, No. 3, pp. 730–752.
L.Holloway and B.Krogh(1992), Properties of Behavioral Models for a Class of Hybrid Dynamical Systems, Proc. of the 31th Conf. Decision and Control, pp.3752–3757.
J.Y. Hung, W. Gao, and J.C. Hung(1993), Variable Structure Control: A Survey, IEEE Trans. on Industrial Electronics, Vol. 40, No. 1, pp.2–22.
W.Kohn and A.Nerode(1992), Multiple Agent Autonomous Hybrid Control Systems, Proc. of the 31th Conf. Decision and Control, pp.2956–2966.
M.D. Lemmon, J.A. Stiver, and P.J. Antsaklis(1993), Learning to Coordinate Control Polices of Hybrid Systems, Proc. of American Control Conf., pp.31–35.
J.Lu, L.Liao, A.Nerode and J.H.Taylor(1993), Optimal Control of Systems with Continuous and Discrete state, Proc. of the 32th Conf. Decision and Control, pp. 2292–2297.
P. Peleties and R. DeCarlo(1989), A Modeling Strategy with Event Structures for Hybrid Systems, Proc. of the 28th Conf. Decision and Control, pp.1308–1313.
J.A. Stiver and P.J. Antsaklis(1992), Modeling and analysis of hybrid control Systems, Proc. of the 31th Conf. Decision and Control, pp.3748–3751.
J.A. Stiver and P.J. Antsaklis(1993), On the Controllability of Hybrid Control Systems, Proc. of the 32th Conf. Decision and Control, pp.294–299.
P.J. Ramadge and W.M. Wonham(1987), Supervisory Control of A Class of Discrete Event Processes, SIAM J. Control and Optimization, Vol.25, No.1, pp.206–230.
W.M. Wonham and P.J. Ramadge(1987), On the supremal controllable sublanguage of a given language, SIAM J. Control and Optimization, Vol.25, No.3, pp.637–659
X. Feng, K.A. Loparo, Y. Ji, H.J. Chizeck(1992), Stochastic Stability Properties of Jump linear Systems, IEEE Tr. on AC, Vol. 37, No. 1, pp 38–53.
R. Brockett(1994), Language Driven Hybrid Systems, Proc. of the 33rd Conf. Decision and Control, pp.4210–4214.
B. Lennartson, B. Egardt, and M. Tittus(1994), Hybrid Systems in Process Conrol, Proc. of the 33rd Conf. Decision and Control, pp.3587–3592.
J.A. Stiver, P.J. Antsaklis, and M.D. Lemmon(1994), Digital Control from a Hybrid Perspective, Proc. of the 33rd Conf. Decision and Control, pp.4241–4246.
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© 1996 Springer-Verlag Berlin Heidelberg
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Park, H.S., Kim, Y.S., Kwon, W.H., Lee, S.J. (1996). Model and stability of hybrid linear system. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds) Hybrid Systems III. HS 1995. Lecture Notes in Computer Science, vol 1066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020965
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DOI: https://doi.org/10.1007/BFb0020965
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