IJCMP | The Bound of Reachable Sets Estimation for Neutral Markovian Jump Systems with Disturbances

Indexing and Abstracting

The Bound of Reachable Sets Estimation for Neutral Markovian Jump Systems with Disturbances

Changchun Shen , Guanke Ma , Jinlin Yang

International Journal of Chemistry, Mathematics And Physics(IJCMP), Vol-4,Issue-3, May - June 2020, Pages 57-64 , 10.22161/ijcmp.4.3.4

Download | Downloads : | Total View : 927

Abstract:

The problem of finding an bound of reachable sets for neutral markovian jump systems with bounded peak disturbances is studied in this paper. Up to now, the result related to the bound of reachable sets was rarely proposed for neutral markovian jump systems. Based on the modified Lyapunov-Krasovskii type functional and linear matrix inequality technology, we obtain some delay-dependent results expressed in the form of matrix inequalities containing only one non-convex scalar. Numerical examples are given to illustrate our theoretical results.

Keywords:

Reachable set, linear neutral system, Lyapunov-Krasovskii, Linear matrix inequalities.

References:

[1] Y. Ji, H. Chizeck, “Controllability, stabilizability and continuous-time Markovian jump linear quadratic control,” IEEE Trans. Autom. Control, vol.35, pp.777-788, 1990.
[2] W.-H. Chen, Z.-H. Guan, X.-M. Lu, “Robust H1 control of neutral delay system switch Markovian jumping parameters,” Control Theory Appl., Vol.20, pp.776-778, 2003.
[3] L.L. Xiong, J.K. Tian, X.Z. Liu, “Stability analysis for neutral Markovian jump systems with partially unknown transition probabilities,” J. Frankl. Inst., vol.349, pp.2193-2214, 2012.
[4] S.Y. Xing, F.Q. Deng, “Delay-dependent H filtering for discrete singular Markov jump systems with Wiener process and partly unknown transition probabilities,” J. Frankl. Inst., vol.355, pp.6062-6086, 2018.
[5] A.N. Vargas, M.A.F. Montezuma, X.H. Liu, R.C.L.F. Oliveira, “Robust stability of Markov jump linear systems through randomized evaluations, ” Appl. Math. Comput., vol.346, pp.87-294, 2019.
[6] O.M. Kwon, Ju H. Park, S.M. Lee, “On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays,” Appl. Math. Comput., vol.197, pp.864-873, 2008.
[7] C.C. Shen, S.M. Zhong, “New delay dependent robust stability criterion for uncertain neutral systems with time-varying delay and nonlinear uncertainties,” Chaos, Solitons Fractals, vol.40, pp.2277-2285, 2009.
[8] Y.L. Dong, W.J. Liu, T.R. Li, S. Liang, “Finite-time boundedness analysis and H control for switched neutral systems with mixed time-varying delays,” J. Frankl. Inst., vol.354, pp.787-811, 2017.
[9] P. Balasubramaniam etc. “Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters,” Appl. Math. Comput., vol.216, pp.3396-3407, 2010.
[10] L.L. Xiong, J.K. Tian, X.Z. Liu, “Stability analysis for neutral Markovian jump systems with partially unknown transition probabilities,” J. Frankl. Inst., vol.2012, pp.2193-2214, 349.
[11] W.M. Chen, B.Y. Zhang, Q. Ma, “Decay-rate-dependent conditions for exponential stability of stochastic neutral systems with Markovian jumping parameters,” Appl. Math. Comput., vol.321, pp.93-105, 2018.
[12] T. Wu, L.L. Xiong, J.D. Cao, Z.X. Liu, H.Y. Zhang, “New stability and stabilization conditions for stochastic neural networks of neutral type with Markovian jumping parameters,” J. Frankl. Inst., vol.355, pp.8462-8483, 2018.
[13] S. Boyd, L. El Ghaoui, E. Feron, V. “Balakrishnan, Linear matrix inequalities in systems and control theory,” Philadelphia PA: SIAM, 1994.
[14] Al. Claudio, “The reachable set of a linear endogenous switching system,” Syst. Control Lett., vpl.47, pp.343-353, 2002.
[15] T. Pecsvaradi, “Reachable Sets for Linear Dynamical Systems,” Informat. Control, vol.19, pp.319-344, 1971.
[16] E. Fridman, “On reachable sets for linear systems with delay and bounded peak inputs,” Automatica, vol.39, pp.2005-2010, 2003.
[17] T. Hu, Z. Lin, “Control Systems with Actuator Saturation: Analysis and Design,” Boston: Birkhauser, 2001.
[18] J.H. Kim, “Improved ellipsoidal bound of reachable sets for time-delayed linear systems with disturbances,” Automatica, vol.44 pp.2940-2943, 2008.
[19] T.I. Seidman, “Time-Invariance of the Reachable Set for Linear Control Problems,” J. Math. Anal. Appl., vol.72, pp.17-20, 1979.
[20] Z.Q. Zuo, D.W.C. Ho, Y.J. Wang, “Reachable set bounding for delayed systems with polytopic uncertainties: The maximal Lyapunov-Krasovskii functional approach,” Automatica, vol.46, pp.949-952, 2010.
[21] C.C. Shen, S.M. Zhong, “The ellipsoidal bound of reachable sets for linear neutral systems with disturbances,” J. Frankl. Inst., 348 (2011) 2570-2585.
[22] W.J. Lin, Y. He, M. Wu, Q.P. Liu, “Reachable set estimation for Markovian jump neural networks with time-varying delay,” Neural Networks, pp.108, 527-532, 2018.