Static Output Feedback Control for Nonlinear Time-Delay Semi-Markov Jump Systems Based on Incremental Quadratic Constraints
Abstract
:1. Introduction
- The nonlinearity satisfying IQC is introduced into the output feedback of SMJS, and a new framework with an IQC nonlinear time-delay SMJS static output feedback control problem is proposed, which expands the application scope of SMJS.
- A class of augmented Lyapunov–Krasovskii functional containing more delay information is constructed, and an improved matrix transformation is used to preprocess the system model, making it easier to solve the output feedback controller. These methods are more versatile and can achieve less conservative stability conditions.
- The matrix inequality is processed by the projection theorem and the convex set principle, and some parameter-dependent sufficient criteria are obtained to ensure that the output feedback can stabilize the nonlinear time-delay SMJS. Then, the output feedback controller can be obtained by the linear matrix inequality (LMI). Finally, two case examples are provided to verify the effectivity of the proposed control algorithm.
2. Problem Formulation
3. Main Results
4. Numerical Examples
- Example 1
- Mode 1:
- Mode 2:
- Mode 3:
- Example 2
- Mode 1:
- Mode 2:
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Chavez-Fuentes, J.; Costa, E.; Mayta, J.; Terra, M. Regularity and stability analysis of discrete- time Markov jump linear singular systems. Automatica 2017, 76, 32–40. [Google Scholar] [CrossRef]
- Feng, X.; Loparo, K.; Ji, Y.; Chizeck, H. Stochastic stability properties of jump linear systems. IEEE Trans. Autom. Control 1992, 37, 38–53. [Google Scholar] [CrossRef]
- You, K.; Fu, M.; Xie, L. Mean square stability for Kalman filtering with Markovian packet losses. Automatica 2011, 47, 2647–2657. [Google Scholar] [CrossRef]
- Shi, Y.; Yu, B. Output feedback stabilization of networked control systems with random delays modeled by Markov chains. IEEE Trans. Autom. Control 2009, 54, 1668–1674. [Google Scholar]
- Wu, N.E. Coverage in fault-tolerant control. Automatica 2004, 40, 537–548. [Google Scholar] [CrossRef]
- Jacquemart, D.; Morio, J. Conflict probability estimation between aircraft with dynamic importance splitting. Saf. Sci. 2013, 51, 94–100. [Google Scholar] [CrossRef]
- Cheng, J.; Xie, L.; Park, J.H.; Yan, H. Protocol-based output-feedback control for semi-markov jump systems. IEEE Trans. Autom. Control 2022, 67, 4346–4353. [Google Scholar] [CrossRef]
- Tian, Y.; Yan, H.; Zhang, H.; Zhan, X.; Peng, Y. Resilient static output feedback control of linear semi-Markov jump systems with incomplete semi-Markov kernel. IEEE Trans. Autom. Control 2020, 66, 4274–4281. [Google Scholar] [CrossRef]
- Tian, Y.; Yan, H.; Zhang, H.; Cheng, J.; Shen, H. Asynchronous output feedback control of hidden semi-markov jump systems with random mode-dependent delays. IEEE Trans. Autom. Control 2021, 67, 4107–4114. [Google Scholar] [CrossRef]
- Chen, H.; Zong, G.; Zhao, X.; Gao, F.; Shi, K. Secure filter design of fuzzy switched CPSs with mismatched modes and application: A multi-domain event-triggered strategy. IEEE Trans. Ind. Inform. 2023, 1–10. [Google Scholar] [CrossRef]
- Zong, G.; Yang, D.; Lam, J.; Song, X. Fault-tolerant control of switched LPV systems: A bumpless transfer approach. IEEE Trans. Mechatron. 2022, 27, 1436–1446. [Google Scholar]
- Schioler, H.; Leth, J.; Simonsen, M. Stochastic stability of diffusions with semi-Markovian switching. In Proceedings of the 54th IEEE Conference on Decision and Control, Osaka, Japan, 14 December 2015. [Google Scholar]
- Wang, B.; Zhu, Q. Stability analysis of semi-Markov switched stochastic systems. Automatica 2018, 94, 72–80. [Google Scholar] [CrossRef]
- Zhang, H.; Qiu, Z.; Xiong, L. Stochastic stability criterion of neutral-type neural networks with additive time-varying delay and uncertain semi-Markov jump. Neurocomputing 2019, 333, 395–406. [Google Scholar] [CrossRef]
- Shen, H.; Chen, M.; Wu, Z.-G.; Cao, J.; Park, J.H. Reliable event-triggered asynchronous extended passive control for semi-Markov jump fuzzy systems and its application. IEEE Trans. Fuzzy Syst. 2019, 28, 1708–1722. [Google Scholar] [CrossRef]
- Qi, W.; Park, J.H.; Zong, G.; Cao, J.; Cheng, J. Filter for positive stochastic nonlinear switching systems with phase-type semi-Markov parameters and application. IEEE Trans. Syst. Man Cybern. Syst. 2021, 52, 2225–2236. [Google Scholar] [CrossRef]
- Wang, J.; Chen, M.; Shen, H. Event-triggered dissipative filtering for networked semi-Markov jump systems and its applications in a mass-spring system model. Nonlinear Dyn. 2017, 87, 2741–2753. [Google Scholar] [CrossRef]
- Shen, H.; Li, F.; Cao, J.; Wu, Z.G.; Lu, G. Fuzzy-model-based output feedback reliable control for network-based semi-Markov jump nonlinear systems subject to redundant channels. IEEE Trans. Cybern. 2020, 50, 4599–4609. [Google Scholar] [CrossRef] [PubMed]
- Shen, H.; Li, F.; Cao, J.; Wu, Z.G.; Lu, G. Song. Resilient and robust control for event-triggered uncertain semi-Markov jump systems against stochastic cyber attacks. Int. J. Robust Nonlinear Control 2022, 32, 3847–3871. [Google Scholar]
- Tian, Y.; Yan, H.; Zhang, H.; Yang, S.X.; Li, Z. Observed-based finite-time control of nonlinear semi-Markovian jump systems with saturation constraint. IEEE Trans. Syst. Man Cybern. Syst. 2020, 51, 6639–6649. [Google Scholar] [CrossRef]
- Yan, S.; Gu, Z.; Park, J.H.; Xie, X. Adaptive memory-event-triggered static output control of T-S fuzzy wind turbine systems. IEEE Trans. Fuzzy Syst. 2022, 30, 3894–3904. [Google Scholar] [CrossRef]
- Yang, D.; Zong, G.; Su, S.-F. H∞ tracking control of uncertain Markovian hybrid switching systems: A fuzzy switching dynamic adaptive control approach. IEEE Trans. Cybern. 2022, 66, 3111–3122. [Google Scholar] [CrossRef]
- Yan, S.; Gu, Z.; Park, J.H.; Xie, X. Distributed-delay-dependent stabilization for networked interval type-2 fuzzy systems with stochastic delay and actuator saturation. IEEE Trans. Syst. Man Cybern. Syst. 2022, 1–11. [Google Scholar] [CrossRef]
- Yan, S.; Gu, Z.; Park, J.H.; Xie, X. Sampled memory-event-triggered fuzzy load frequency control for wind power systems subject to outliers and transmission delays. IEEE Trans. Cybern. 2022, 1–11. [Google Scholar] [CrossRef]
- Wu, T.; Xiong, L.; Cao, J.; Zhang, H. Stochastic stability and extended dissipativity analysis for uncertain neutral systems with semi-Markovian jumping parameters via novel free matrix-based integral inequality. Int. J. Robust Nonlinear Control 2019, 29, 2525–2545. [Google Scholar] [CrossRef]
- Wang, J.; Ma, S.; Zhang, C. Stability analysis and stabilization for nonlinear continuous-time descriptor semi-Markov jump systems. Appl. Math. Comput. 2016, 279, 90–102. [Google Scholar] [CrossRef]
- Yang, J.; Bu, X.; Yu, Q.; Zhu, F. Observer-based controller design for nonlinear semi-Markov switched system with external disturbance. J. Frankl. Inst. 2020, 357, 8435–8453. [Google Scholar] [CrossRef]
- Huang, J.; Yu, L.; Chen, L. Control design for stochastic one-sided Lipschitz differential inclusion system with time delay. Int. J. Syst. Sci. 2018, 49, 2923–2939. [Google Scholar] [CrossRef]
- Açıkmeşe, B.; Corless, M. Observers for systems with nonlinearities satisfying incremental quadratic constraints. Automatica 2011, 47, 1339–1348. [Google Scholar] [CrossRef]
- Huang, J.; Shi, Y. Stochastic stability and robust stabilization of semi-Markov jump linear systems. Int. J. Robust Nonlinear Control 2013, 23, 2028–2043. [Google Scholar] [CrossRef]
- Seuret, A.; Gouaisbaut, F. Hierarchy of LMI conditions for the stability analysis of time-delay systems. Systems. Control Lett. 2015, 81, 1–7. [Google Scholar] [CrossRef]
- Sun, J.; Liu, G.; Chen, J.; Rees, D. Improved delay-range-dependent stability criteria for linear systems with time-varying delays. Automatica 2010, 46, 466–470. [Google Scholar] [CrossRef]
- Seuret, A.; Gouaisbaut, F.; Fridman, E. Stability of systems with fast-varying delay using improved Wirtinger’s inequality. In Proceedings of the 52th IEEE Conference on Decision and Control, Florence, Italy, 10–13 December 2013. [Google Scholar]
- Tian, J.; Ma, S.; Zhang, C. Unknown input reduced-order observer design for one-sided Lipschitz nonlinear descriptor Markovian jump systems. Asian J. Control 2019, 21, 952–964. [Google Scholar] [CrossRef]
- Tuan, H.; Apkarian, P.; Nguyen, T. Robust and reduced-order filtering: New LMI-based characterizations and methods. IEEE Trans. Signal Process. 2001, 49, 2975–2984. [Google Scholar] [CrossRef]
- Shi, P.; Liu, M.; Zhang, L. Fault-Tolerant Sliding-Mode-Observer Synthesis of Markovian Jump Systems Using Quantized Measurements. IEEE Trans. Ind. Electron. 2015, 62, 5910–5918. [Google Scholar] [CrossRef]
- Zhang, M.; Huang, J.; Zhang, Y. Stochastic stability analysis of nonlinear semi-Markov jump systems with time delays and incremental quadratic constraints. J. Frankl. Inst. 2021. [Google Scholar] [CrossRef]
Parameters | i = 1 | i = 2 | i = 3 |
---|---|---|---|
−0.5 | 1.5 | 2 | |
0.15 | 0.15 | 0.15 | |
0.12 | 0.2 | 0.2 | |
0.15 | 0.13 | 0.15 | |
−1.5 | −1.3 | −0.15 | |
0.2 | 0.3 | 0.4 | |
0.2 | 0.3 | 0.4 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Zhou, Y.; Ji, X. Static Output Feedback Control for Nonlinear Time-Delay Semi-Markov Jump Systems Based on Incremental Quadratic Constraints. Math. Comput. Appl. 2023, 28, 30. https://doi.org/10.3390/mca28020030
Zhou Y, Ji X. Static Output Feedback Control for Nonlinear Time-Delay Semi-Markov Jump Systems Based on Incremental Quadratic Constraints. Mathematical and Computational Applications. 2023; 28(2):30. https://doi.org/10.3390/mca28020030
Chicago/Turabian StyleZhou, Yang, and Xiaofu Ji. 2023. "Static Output Feedback Control for Nonlinear Time-Delay Semi-Markov Jump Systems Based on Incremental Quadratic Constraints" Mathematical and Computational Applications 28, no. 2: 30. https://doi.org/10.3390/mca28020030