International Journal of Robust and Nonlinear Control

RESEARCH ARTICLE

Estimation of attraction domain of nonlinear systems with saturated impulses and input disturbances

Hongjuan Wu

Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, China

School of Computer Science and Engineering, Chongqing Three Gorges University, Chongqing, China

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Chuandong Li,

Corresponding Author

Chuandong Li

[email protected]

orcid.org/0000-0002-3582-1621

Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, China

Correspondence Chuandong Li, Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China.

Email: [email protected]

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Zhilong He,

Zhilong He

Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, China

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Yinuo Wang,

Yinuo Wang

Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, China

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Hongjuan Wu,

Hongjuan Wu

Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, China

School of Computer Science and Engineering, Chongqing Three Gorges University, Chongqing, China

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Chuandong Li,

Corresponding Author

Chuandong Li

[email protected]

orcid.org/0000-0002-3582-1621

Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, China

Email: [email protected]

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Zhilong He,

Zhilong He

Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, China

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Yinuo Wang,

Yinuo Wang

Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, China

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First published: 21 September 2021

https://doi.org/10.1002/rnc.5783

Citations: 1

Funding information: National Key Research and Development Project, 2018AAA0100101; National Natural Science Foundation of China, 61633011; 61873213; Scientific and Technological Research Program of Chongqing Municipal Education Commission, KJQN201901205

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Abstract

In this article, the estimation of attraction domain of nonlinear systems with saturated impulses and input disturbances is investigated. The sufficient conditions which can ensure the robust convergence of a class of nonlinear dynamical systems for every initial condition in the attraction domain are established. Moreover, some optimization problems are proposed to design the control gain so as to enlarge the size of the estimation of attraction domain as much as possible with a prespecified decay rate. In addition, the exponential stabilization and the estimation of attraction domain for nonlinear dynamical systems under this saturated impulsive control without disturbances are also studied. Finally, simulation results for a chaotic oscillator are displayed to show the effectiveness and feasibility of our results.

CONFLICT OF INTEREST

The authors declare that there is no conflict of interest regarding the publication of this paper.

Open Research

DATA AVAILABILITY STATEMENT

The data used to support the findings of this study are available from the corresponding author upon reasonable request.

REFERENCES

1Tarbouriech S, Garcia G, Silva JMG, Queinnec I. Stability and Stabilization of Linear Systems with Saturating Actuators. Springer Science & Business Media; 2011.
10.1007/978-0-85729-941-3
Google Scholar
2Chen Y, Wang Z, Fei S, Han Q. Regional stabilization for discrete time-delay systems with actuator saturations via a delay-dependent polytopic approach. IEEE Trans Automat Contr. 2019; 64(3): 1257-1264.
10.1109/TAC.2018.2847903
Web of Science® Google Scholar
3Jing B, Hong KL. Stability and attraction domains of traffic equilibria in a day-to-day dynamical system formulation. Transp Res B Methodol. 2010; 44(1): 90-107.
10.1016/j.trb.2009.06.007
Web of Science® Google Scholar
4Li Y, Lin Z. The maximal contractively invariant ellipsoids for discrete-time linear systems under saturated linear feedback. Automatica. 2017; 76: 336-344.
10.1016/j.automatica.2016.10.007
Web of Science® Google Scholar
5Li Y, Lin Z. Improvements to the linear differential inclusion approach to stability analysis of linear systems with saturated linear feedback. Automatica. 2013; 49(3): 821-828.
10.1016/j.automatica.2012.12.002
Web of Science® Google Scholar
6Lin Z, Li Y. Estimation of domain of attraction for linear systems with actuator saturation. Control Decis. 2018; 33(5): 824-834. (in Chinese).
Google Scholar
7Li C, Wu S, Feng G, Liao X. Stabilizing effects of impulses in discrete-time delayed neural networks. IEEE Trans Neural Netw. 2011; 22(2): 323-329.
10.1109/TNN.2010.2100084
CAS PubMed Web of Science® Google Scholar
8Hu W, Zhu Q, Karimi HR. Some improved Razumikhin stability criteria for impulsive stochastic delay differential systems. IEEE Trans Automat Contr. 2019; 64(12): 5207-5213.
10.1109/TAC.2019.2911182
Web of Science® Google Scholar
9Feng Y, Li C, Huang T. Sandwich control systems with impulse time windows. Int J Mach Learn Cybern. 2017; 8(6): 2009-2015.
10.1007/s13042-016-0580-5
Web of Science® Google Scholar
10Li H, Li C, Huang J. A hybrid impulsive and sampled-data control framework for a class of nonlinear dynamical systems with input constraints. Nonlinear Anal Hybrid Syst. 2020; 36: 100881.
10.1016/j.nahs.2020.100881
Web of Science® Google Scholar
11Hu W, Zhu Q. Stability criteria for impulsive stochastic functional differential systems with distributed-delay dependent impulsive effects. IEEE Trans Syst Man Cybern Syst. 2019; 1-6.
Web of Science® Google Scholar
12Li L, Li C, Li H. Fully state constraint impulsive control for non-autonomous delayed nonlinear dynamic systems. Nonlinear Anal Hybrid Syst. 2018; 29: 383-394.
10.1016/j.nahs.2018.03.008
Web of Science® Google Scholar
13Li H, Li C, Zhang W, Cao Z. Exponential stabilization for nonlinear coupled dynamical systems via impulsive and sampled-data control with input constraints. Int J Robust Nonlinear Control. 2019; 29(6): 6126-6144.
10.1002/rnc.4708
Web of Science® Google Scholar
14Shen Z, Li C, Li H, Cao Z. Estimation of the domain of attraction for discrete-time linear impulsive control systems with input saturation. Appl Math Comput. 2019; 362: 124502.
10.1016/j.amc.2019.06.016
Web of Science® Google Scholar
15Hu T, Lin Z, Chen BM. An analysis and design method for linear systems subject to actuator saturation and disturbance. Automatica. 2002; 38(2): 351-359.
10.1016/S0005-1098(01)00209-6
Web of Science® Google Scholar
16Oucheriah S. Robust exponential convergence of a class of linear delayed systems with bounded controllers and disturbances. Automatica. 2006; 42: 1863-1867.
10.1016/j.automatica.2006.05.023
Web of Science® Google Scholar
17Li Y, Lin Z. An asymmetric Lyapunov function for linear systems with asymmetric actuator saturation. Int J Robust Nonlinear Control. 2018; 28(5): 1624-1640.
10.1002/rnc.3976
Web of Science® Google Scholar
18Cai X, Zhong S, Wang J, Shi K. Robust $urn:x-wiley:10498923:media:rnc5783:rnc5783-math-0404$ control for uncertain delayed $urn:x-wiley:10498923:media:rnc5783:rnc5783-math-0405$ - $urn:x-wiley:10498923:media:rnc5783:rnc5783-math-0406$ fuzzy systems with stochastic packet dropouts. Appl Math Comput. 2020; 385: 125432.
10.1016/j.amc.2020.125432
Web of Science® Google Scholar
19Huang T, Li C, Duan S, Starzyk JA. Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects. IEEE Trans Neural Netw Learn Syst. 2012; 23(6): 866-875.
10.1109/TNNLS.2012.2192135
PubMed Web of Science® Google Scholar
20Wei Y, Liu GP. Composite control for switched impulsive time-delay systems subject to actuator saturation and multiple disturbances. Nonlinear Anal Hybrid Syst. 2020; 35: 100825.
10.1016/j.nahs.2019.100825
Web of Science® Google Scholar
21Qian Y, Xiang Z, Karimi HR. Disturbance tolerance and rejection of discrete switched systems with time-varying delay and saturating actuator. Nonlinear Anal Hybrid Syst. 2015; 16(2015): 81-92.
10.1016/j.nahs.2014.11.001
Web of Science® Google Scholar
22Guo B, Chen Y. Adaptive fast sliding mode fault tolerant control integrated with disturbance observer for spacecraft attitude stabilization system. ISA Trans. 2019; 94: 1-9.
10.1016/j.isatra.2019.04.014
PubMed Web of Science® Google Scholar
23Yang J, Lu J, Lou J, Liu Y. Synchronization of drive-response Boolean control networks with impulsive disturbances. Appl Math Comput. 2020; 364: 124679.
10.1016/j.amc.2019.124679
Web of Science® Google Scholar
24Jiang H., Zhou C., Yu J., Xu C.. Delay-dependent exponential stabilization of nonlinear delay systems subject to impulsive disturbance of input. Proceedings of the 27th Chinese Control Conference; 2008.
Google Scholar
25Amato F, Ambrosino R, Tommasi GD, Merola A. Estimation of the domain of attraction for a class of hybrid systems. Nonlinear Anal Hybrid Syst. 2011; 5(3): 573-582.
10.1016/j.nahs.2010.12.005
Web of Science® Google Scholar
26Li C, Feng G, Huang T. On hybrid impulsive and switching neural networks. IEEE Trans Syst Man Cybern B (Cybern). 2008; 38(6): 1549-1560.
10.1109/TSMCB.2008.928233
Google Scholar
27Hu W, Zhu Q. Stability analysis of impulsive stochastic delayed differential systems with unbounded delays. Syst Control Lett. 2020; 136: 104606.
10.1016/j.sysconle.2019.104606
Web of Science® Google Scholar
28Feng Y, Li C, Huang T. Periodically multiple state-jumps impulsive control systems with impulse time windows. Neurocomputing. 2016; 193: 7-13.
10.1016/j.neucom.2016.01.059
Web of Science® Google Scholar
29Sanchez EN, Perez JP. Input-to-state stability (ISS) analysis for dynamic neural networks. IEEE Trans Circuits Syst I Fund Theory Appl. 1999; 46(11): 1395-1395.
10.1109/81.802844
Google Scholar
30Moore RE, Bloom F. Linear Matrix Inequalities in System and Control Theory. SIAM; 1994.
Google Scholar
31Hu T, Lin Z. Control Systems with Actuator Saturation Analysis and Design. Springer Science and Business Media LLC; 2001.
10.1007/978-1-4612-0205-9
Google Scholar
32Shil'nikov LP. Chua's circuit: rigorous results and future problems. IEEE Trans Circuits Syst I Fund Theory Appl. 1993; 40(10): 784-786.
10.1109/81.246153
Google Scholar