STATE-FEEDBACK CONTROL OF SWITCHED NONLINEAR SYSTEMS WITH TIME-VARYING DELAY

His paper investigates the output tracking problem for a class of switched nonlinear systems with timevarying delays. Such systems are characterized by switching among multiple subsystems as well as the presence of delays that vary over time, which significantly complicates their dynamics. The combined effects of switching and time delays may result in degraded control performance, oscillatory behaviors, and, in some cases, loss of stability. Therefore, the synthesis of effective control laws for such systems constitutes an important and challenging problem in modern control theory. A state-feedback control law is proposed to achieve the desired output tracking performance. The proposed approach is designed to ensure the boundedness of all signals in the closed-loop system in the presence of nonlinearities, switching, and timevarying delays. The stability properties of the system and the dynamics of the tracking error are analyzed using Lyapunov-Krasovskii functionals, which allow the influence of time delays on system behavior to be explicitly taken into account. It is shown that an appropriate selection of the control gains can significantly reduce the destabilizing effects caused by switching and time-varying delays. To validate the theoretical results, numerical simulation results are presented, demonstrating the effectiveness of the proposed control strategy and confirming its applicability to a broad class of switched nonlinear systems with time-varying delays.

1. Khalil H.K. Nonlinear systems. 3rd ed / H.K. Khalil. – Upper Saddle River: Prentice Hall, 2002. – 750 p.

2. Fridman E. Introduction to time-delay systems: analysis and control / E. Fridman. – Basel: Birkhäuser, 2014. – 352 p.

3. Sun Z. Switched linear systems: control and design / Z. Sun, S.S. Ge. – London: Springer, 2011. – 312 p.

4. Liberzon D. Switching in systems and control / D. Liberzon. Boston: Birkhäuser, 2003. – 256 p.

5. Zhang W. Output tracking control for switched nonlinear systems with time-varying delay / W. Zhang, M. Chen, Y. Li // Nonlinear Analysis: Hybrid Systems. – 2018. – Vol. 29. – P. 257-270.

6. Li X. Stability and control of nonlinear systems with time-varying delays / X. Li, R. Rakkiyappan // IEEE Transactions on Automatic Control. – 2016. – Vol. 61, № 6. – P. 1488-1493.

7. He Y. Delay-dependent stability criteria for nonlinear systems with time-varying delays / Y. He, M. Wu, J.-H. She // Automatica. – 2015. – Vol. 52. – P. 132-137.

8. Wang Y. Switched nonlinear systems with time-varying delay: stability and control / Y. Wang, X. Liu // ISA Transactions. – 2019. – Vol. 85. – P. 1-10.

9. Park P. Lyapunov-Krasovskii functionals for time-delay systems: a new approach / P. Park, J. Ko, C. Jeong // Systems & Control Letters. – 2016. – Vol. 97. – P. 1-8.

10. Chen W. State-feedback control for switched nonlinear systems with delays / W. Chen, Z. Li // IEEE Access. – 2020. – Vol. 8. – P. 112345-112356.

11. Zhao X. Stability and stabilization of switched nonlinear systems with time-varying delays / X. Zhao, L. Zhang, P. Shi // IEEE Transactions on Automatic Control. – 2017. – Vol. 62, № 7. – P. 3623-3629.

12. Yang X. Robust stability of switched nonlinear systems with time-varying delay / X. Yang, X. Li, J. Cao // Nonlinear Dynamics. – 2018. – Vol. 93. – P. 1875-1887.

13. Zhang H. Output feedback control for switched nonlinear systems with time-varying delays / H. Zhang, Z. Wang, Y. Liu // International Journal of Control. – 2019. – Vol. 92, № 9. – P. 2074-2085.

14. Zhou B. Output regulation of switched nonlinear systems with time delays / B. Zhou, Z. Lin // Automatica. – 2021. – Vol. 129. – Art. № 109615.