Practical Exponential Stability of Two Dimensional Nonlinear Switched Positive Systems in the Roesser Model

Journal of Systems Science and Complexity - Tập 36 - Trang 1103-1115 - 2023
Jie Zhang1, Yuangong Sun1
1School of Mathematical Sciences, University of Jinan, Jinan, China

Tóm tắt

This paper deals with the practical exponential stability of two-dimensional (2-D) nonlinear switched positive systems with impulse, disturbance and all modes unstable. Under the mode-dependent interval dwell time switching, new criteria such that 2-D nonlinear switched positive systems achieve practical exponential stability are derived. Furthermore, the explicit upper bound and convergence rate of the system state are estimated explicitly. Numerical examples indicate the correctness and effectiveness of the obtained results.

Tài liệu tham khảo

Xiang Z R and Huang S P, Stability analysis and stabilization of discrete-time 2D switched systems, Circuits Dystem and Signal Processing, 2013, 32(1): 401–414. Chesi G and Middleton R H, Robust stability and performance analysis of 2D mixed continuous-discrete-time systems with uncertainty, Automatica, 2010, 67: 233–243. Chen X M, Lam J, Gao H J, et al., Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions, Multidimensional Systems and Signal Processing, 2013, 24(3): 395–415. Roesser R P, A discrete state-space model for linear image processing, IEEE Transactions on Automatic Control, 1975, 20(1): 1–10. Fornasini E and Marchesini G, State-space realization theory of two dimensional filters, IEEE Transactions on Automatic Control, 1976, 21(4): 481–491. Ooba T, Asymptotic stability of two-dimensional discrete systems with saturation nonlinearities, IEEE Transactions on Circuits and Systems I: Regular Papers, 2013, 60(1): 178–188. Liu X, Yu W, and Wang L, Necessary and sufficient asymptotic stability criterion for 2-D positive systems with time-varying state delays described by Roesser model, IET Control Theory and Applications, 2011, 5(5): 663–668. Zhou P, Zhang L, Zhang S, et al., Observer-based adaptive fuzzy finite-time control design with prescribed performance for switched pure-feedback nonlinear systems, IEEE Access, 2020, 9: 69481–69491. Chang Y, Zhou P, Niu B, et al., Switched-observer-based adaptive output-feedback control design with unknown gain for pure-feedback switched nonlinear systems via average dwell time, International Journal of Systems Science, 2021, 52(9): 1731–1745. Sun Y G, Tian Y Z, and Xie X J, Stabilization of positive switched linear systems and its application in consensus of multi-agent systems, IEEE Transactions on Automatic Control, 2017, 62(12): 6608–6613. Sun Y G and Wu Z R, On the existence of linear copositive Lyapunov functions for 3-dimensional switched positive linear systems, Journal of Franklin Institute, 2013, 350(6): 1379–1387. Liu X W, Stability analysis of a class of nonlinear positive switched systems with delays, Nonlinear Analysis: Hybrid System, 2015, 16: 1–12. Zhang J F, Liu L Y, Li S, et al., Event-triggered L1-gain control of nonlinear positive switched systems, Journal of Systems Science and Complexity, 2021, 34(3): 873–898. Zhang N, Sun Y G, and Meng F W, State bounding for switched homogeneous positive nonlinear systems with exogenous input, Nonlinear Analysis: Hybrid System, 2018, 29: 363–372. Zhang J and Sun Y G, Reachable set estimation for switched nonlinear positive systems with impulse and time delay, International Journal of Robust and Nonlinear Control, 2020, 30(8): 3332–3343. Duan Z X, Xiang Z R, and Karimi H R, Delay-dependent exponential stabilization of positive 2D switched state-delayed systems in the Roesser model, Information Sciences, 2014, 272: 173–184. Kaczorek T, Positive switched 2D linear systems described by the Roesser models, European Journal of Control, 2012, 18(3): 239–246. Hien L V and Trinh H, Exponential stability of two-dimensional homogeneous monotone systems with bounded directional delays, TEEE Transactions on Automatic Control, 2018, 63(8): 2694–2700. Tian D D, Liu S T, and Wang W, Global exponential stability of 2D switched positive nonlinear systems described by the Roesser model, International Journal of Robust and Nonlinear Control, 2019, 29(7): 2272–2282. Benzaouia A, Hmamed A, Tadeo F, et al., Stabilisation of discrete 2D time switching systems by state feedback control, International Journal of Systems Science, 2011, 42(3): 479–487.