Stability analysis of some classes of nonlinear switched systems with time delay

References

• Aizerman, M. A., & Gantmacher, F. R. (1963). Absolute stability of control systems. San Francisco, CA: Holden-Day.
   Google Scholar
• Aleksandrov, A., & Aleksandrova, E. (2016). Asymptotic stability conditions for a class of hybrid mechanical systems with switched nonlinear positional forces. Nonlinear Dynamics, 83(4), 2427–2434.
   Web of Science ®Google Scholar
• Aleksandrov, A. Y., Aleksandrova, E. B., Zhabko, A. P., & Dai, G. (2016). Stability analysis and estimation of the convergence rate of solutions for nonlinear time-delay systems. In J. Koton S. Andreev (Eds.) Proceedings of the Intern. Congress on Ultra Modern Telecommunications and Control Systems and Workshops. IEEE. (pp. 67–72). Brno.
   Google Scholar
• Aleksandrov, A. Yu., Chen, Y., Platonov, A. V., & Zhang, L. (2011). Stability analysis for a class of switched nonlinear systems. Automatica, 47, 2286–2291.
   Web of Science ®Google Scholar
• Aleksandrov, A. Yu., Hu, Guang-Da, & Zhabko, A. P. (2014). Delay-independent stability conditions for some classes of nonlinear systems. IEEE Transactions on Automatic Control, 59(8), 2209–2214.
   Web of Science ®Google Scholar
• Aleksandrov, A. Yu., & Mason, O. (2014). Absolute stability and Lyapunov–Krasovskii functionals for switched nonlinear systems with time-delay. Journal of the Franklin Institute, 351, 4381–4394.
   Web of Science ®Google Scholar
• Aleksandrov, A. Yu., & Zhabko, A. P. (2012). On the asymptotic stability of solutions of nonlinear systems with delay. Siberian Mathematical Journal, 53(3), 393–403.
   Web of Science ®Google Scholar
• Andrieu, V., Praly, L., & Astolfi, A. (2008). Homogeneous approximation, recursive observer design, and output feedback. SIAM Journal on Control and Optimization, 47(4), 1814–1850.
   Web of Science ®Google Scholar
• Bernuau, E., Polyakov, A., Efimov, D., & Perruquetti, V. (2013). Verification of ISS, iISS and IOSS properties applying weighted homogeneity. Systems & Control Letters, 62, 1159–1167.
   Web of Science ®Google Scholar
• Bhat, S. P., & Bernstein, D. S. (2005). Geometric homogeneity with applications to finite-time stability. Mathematics of Control, Signals and Systems, 17, 101–127.
   Web of Science ®Google Scholar
• Bobylev, N. A., Il'in, A. V., Korovin, S. K., & Fomichev, V. V. (2002). On the stability of families of dynamical systems. Differential Equations, 38(4), 464–470.
   Web of Science ®Google Scholar
• Bokharaie, V., Mason, O., & Verwoerd, M. (2010). D-stability and delay-independent stability of homogeneous cooperative systems. IEEE Transactions on Automatic Control, 55(12), 2882–2885.
   Web of Science ®Google Scholar
• Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. Philadelphia, PA: SIAM.
   Google Scholar
• Campbell, S. A., , & Belir, J. (1993). Multiple-delayed differential equations as models for biological control systems. In V. Lakshmikhantham (Ed.) Proceedings of the World Mathematical Conference. 4, (pp. 3110–3117). Tampa, FL: Walter de Gruyter & Co.
   Google Scholar
• Decarlo, R. A., Branicky, M. S., Pettersson, S., & Lennartson, B. (2000). Perspectives and results on the stability and stabilizability of hybrid systems. Proceedings of the IEEE, 88(7), 1069–1082.
   Web of Science ®Google Scholar
• Duan, Ch., & Wu, F. (2016). New results on switched linear systems with actuator saturation. International Journal of Systems Science, 47(5), 1008–1020.
   Web of Science ®Google Scholar
• Efimov, D., Perruquetti, W., & Richard, J.-P. (2014). Development of homogeneity concept for time-delay systems. SIAM Journal on Control and Optimization, 52(3), 1547–1566.
   Web of Science ®Google Scholar
• Fossen, T. I. (1994). Guidance and control of ocean vehicles. New York, NY: Wiley.
   Google Scholar
• Gopalsamy, K. (1992). Stability and oscillations in delay differential equations of population dynamics. Dordrecht: Kluwer Academic Publishers.
   Google Scholar
• Gu, K., Kharitonov, V. L., & Chen, J. (2003). Stability of Time-Delay systems. Boston, MA: Birkhauser.
   Google Scholar
• Hale, J. K., & Verduyn Lunel, S. M. (1993). Introduction to functional differential equations. New York, NY: Springer–Verlag.
   Google Scholar
• Hopfield, J. J., & Tank, D. W. (1986). Computing with neural circuits: a model. Science, 233, 625–633.
   PubMed Web of Science ®Google Scholar
• Kaszkurewicz, E., & Bhaya, A. (1999). Matrix diagonal stability in systems and computation. Boston, MA: Birkhauser.
   Google Scholar
• Knorn, F., Mason, O., & Shorten, R. (2009). On linear co-positive Lyapunov functions for sets of linear positive systems. Automatica, 45, 1943–1947.
   Web of Science ®Google Scholar
• Krasovskii, N. N. (1963). Problems of the theory of stability of motion. Stanford, CA: Stanford University Press.
   Google Scholar
• Kuang, Y. (1993). Delay differential equations with applications in population dynamics. Boston, MA: Academic Press.
   Google Scholar
• Lakshmikantham, V., Leela, S., & Martynyuk, A. A. (1989). Stability analysis of nonlinear systems. New York, NY: Marcel Dekker.
   Google Scholar
• Liao, X., & Yu, P. (2008). Absolute stability of nonlinear control systems. New York, NY: Springer.
   Google Scholar
• Liberzon, D. (2003). Switching in systems and control. Boston, MA: Birkhauser.
   Google Scholar
• Liberzon, D. (2004). Lie algebras and stability of switched nonlinear systems. In Unsolved Problems in Mathematical Systems and Control Theory (pp. 90–92). Princeton: Princeton University Press.
   Google Scholar
• Marcus, C. W., & Westervelt, R.M. (1989). Stability of analog neural networks with delay. Physical Review, 34, 347–359.
   Web of Science ®Google Scholar
• Mel’nikov, G. I. (1975). [Dynamics of nonlinear mechanical and electromechanical systems]. Leningrad: Mashinostroenie. Russian.
   Google Scholar
• Niculescu, S. (2001). Delay effects on stability: A robust control approach. lecture notes in control and information science. New York, NY: Springer.
   Google Scholar
• Persidskii, S. K. (1969). Problem of absolute stability. Automation and Remote Control, (12), 1889–1895.
   Web of Science ®Google Scholar
• Richard, J. -P. (2003). Time-delay systems: An overview of some recent advances and open problems. Automatica, 39, 1667–1694.
   Web of Science ®Google Scholar
• Rosier, L. (1992). Homogeneous Lyapunov function for homogeneous continuous vector field. Systems & Control Letters, 19, 467–473.
   Web of Science ®Google Scholar
• Rouche, N., Habets, P., & Laloy, M. (1977). Stability theory by Lyapunov's direct method. New York,NY: Springer.
   Google Scholar
• Sun, Y. G., Wang, L., & Xie, G. (2006). Stability of switched systems with time-varying delays: Delay-dependent common Lyapunov functional approach. In M.W. Thein (Ed.) Proceedings of the American Control Conference (pp. 1544–1549). Minneapolis, MN: IEEE.
   Google Scholar
• Vassilyev, S. N., & Kosov, A. A. (2011). Analysis of hybrid systems’ dynamics using the common Lyapunov functions and multiple homomorphisms. Automation and Remote Control, 72(6), 1163–1183.
   Web of Science ®Google Scholar
• Veremey, E. I. (2014). Dynamical correction of control laws for marine ships’ accurate steering. Journal of Marine Science and Application, 13, 127–133.
   Google Scholar
• Xia, Y., Liu, G. P., Shi, P., Rees, D., & Thomas, E. J. C. (2007). New stability and stabilization conditions for systems with time-delay. International Journal of Systems Science, 38(1), 17–24.
   Web of Science ®Google Scholar
• Xiang, Z. R., & Xiang, W. M. (2009). Stability analysis of switched systems under dynamical dwell time control approach. International Journal of Systems Science, 40(4), 347–355.
   Web of Science ®Google Scholar
• Zamani, I., Shafiee, M., & Ibeas, A. (2014). Stability analysis of hybrid switched nonlinear singular time-delay systems with stable and unstable subsystems. International Journal of Systems Science, 45(5), 1128–1144.
   Web of Science ®Google Scholar
• Zappavigna, A., Colaneri, P., Geromel, J. C., & Shorten, R. (2010). Dwell time analysis for continuous-time switched linear positive systems. In Richard D. Braatz (Ed.) Proceedings of the American Control Conference (pp. 6256–6261). Baltimore, MD: IEEE.
   Google Scholar
• Zhang, J., Han, Zh., & Huang, J. (2015). Global asymptotic stabilisation for switched planar systems. International Journal of Systems Science, 46(5), 908–918.
   Web of Science ®Google Scholar
• Zhang, L., Liu, Sh., & Lan, H. (2007). On stability of switched homogeneous nonlinear systems. Journal of Mathematical Analysis and Applications, 334(1), 414–430.
   Web of Science ®Google Scholar
• Zubov, V. I. (1964). Methods of A. M. Lyapunov and their applications. Groningen: P. Noordhoff Ltd.
   Google Scholar