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Keywords:
observer-based control; $H_{\infty }$ finite-time boundedness; Lyapunov--Krasovskii functional; discrete-time systems; time-varying delay
observer-based control; $H_{\infty }$ finite-time boundedness; Lyapunov--Krasovskii functional; discrete-time systems; time-varying delay
Summary:
This paper investigates the problem of observer-based finite-time $H_{\infty}$ control for the uncertain discrete-time systems with nonlinear perturbations and time-varying delay. The Luenberger observer is designed to measure the system state. The observer-based controller is constructed. By constructing an appropriated Lyapunov-.Krasovskii functional, sufficient conditions are derived to ensure the resulting closed-loop system is $H_{\infty}$ finite-time bounded via observer-based control. The observer-based controller for the finite-time $H_{\infty}$ control problem is developed. Finally, a numerical example illustrates the efficiency of proposed methods.
References:
[1] Amato, F., Ambrosino, R., Ariola, M., Tommasi, G. De, Pironti, A.: On the finite-time boundedness of linear systems. Automatica 107 (2019), 454-466. DOI | MR 3979026
[2] Amato, F., Darouach, M., Tommasi, G. De: Finite-time stabilizability, detectability, and dynamic output feedback finite-time stabilization of linear systems. IEEE Trans. Automat. Control 62 (2017), 12, 6521-6528. DOI | MR 3743535
[3] Ahmad, S., Rehan, M.: On observer-based control of one-sided Lipschitz systems. J. Frankl. Inst. 353 (2016), 4, 903-916. DOI | MR 3463288
[4] Amato, F., Arioial, M., Dorato, P.: Finite-time control of linear system subject to parametric uncertainties and disturbances. Automatica 37 (2001), 1459-1463. DOI
[5] Cheng, J., Zhu, H., Zhong, S. M., Zeng, Y., Hou, L. Y.: Finite-time $H_{\infty}$ filtering for a class of discrete-time Markovian jump systems with partly unknown transition probabilities. Int. J. Adapt. Control Signal Process. 28 (2014), 1024-1042. DOI | MR 3269858
[6] Dong, Y., Chen, L., Mei, S.: Observer design for neutral-type neural networks with discrete and distributed time-varying delays. Int. J. Adapt. Control Signal Process. 33 (2019), 1, 527-544. DOI | MR 3925377
[7] Dong, Y., Li, T., Mei, S.: Exponential stabilization and $L_{2}$-gain for uncertain switched nonlinear systems with interval time-varying delay. Math. Meth. Appl. Sci. 39 (2016), 3836-3854. DOI | MR 3529387
[8] Dong, Y., Liang, S., Wang, H.: Robust stability and $H_{\infty}$ control for nonlinear discrete-time switched systems with interval time-varying delay. Math. Meth. Appl. Sci. 42 (2019), 1999-2015. DOI | MR 3937647
[9] Dong, Y., Liu, W., Li, T., Liang, S.: Finite-time boundedness analysis and $H_{\infty}$ control for switched neutral systems with mixed time-varying delays. J. Frankl. Inst. 354 (2017), 787-811. DOI | MR 3591977
[10] Dong, Y., Zhang, Y., Zhang, X.: Design of observer-based feedback control for a class of discrete-time nonlinear systems with time-delay. Appl. Comput. Math., 13 (2014), 1, 107-121. MR 3307942
[11] Dorato, P.: Short time stability in linear time-varying system. In: Proc. IRE International Convention Record. Part 4, New York 1961, pp. 83-87.
[12] Karafyllis, I.: Finite-time global stabilization by means of time-varying distributed delay feedback. SIAM J. Control Optim. 45 (2006), 1, 320-342. DOI | MR 2225308
[13] Lin, X., Du, H., Li, S.: Finite-time boundedness and $L_2$ gain analysis for switched delay systems with norm-bounded disturbance. Appl. Math. Comput. 217 (2011), 12, 5982-5993. DOI | MR 2770219
[14] Ma, Y. C., Fu, L., Jing, Y. H., Zhang, Q. L.: Finite-time $H_{\infty}$ control for a class of discrete-time switched singular time-delay systems subject to actuator saturation. Appl. Math. Comput. 261 (2015), 264-283. DOI | MR 3345277
[15] Nguyen, C. M., Pathirana, P. N., Trinh, H.: Robust observer-based control designs for discrete nonlinear systems with disturbances. Europ. J. Control 44 (2018), 65-72. DOI | MR 3907454
[16] Nguyen, C. M., Pathirana, P. N., Trinh, H.: Robust observer design for uncertain one-sided Lipschitz systems with disturbances. Int. J. Robust Nonlinear Control 28 (2018), 1366-1380. DOI | MR 3756748
[17] Nguyen, M. C., Trinh, H.: Observer design for one-sided Lipschitz discrete-time systems subject to delays and unknown inputs. SIAM J. Control Optim 54 (2016), 3, 1585-1601. DOI | MR 3509998
[18] Song, J., He, S.: Robust finite-time $H_{\infty}$ control for one-sided Lipschitz nonlinear systems via state feedback and output feedback. J. Frankl. Inst. 352 (2015), 8, 3250-3266. DOI | MR 3369926
[19] Stojanovic, S. B.: Robust finite-time stability of discrete time systems with interval time-varying delay and nonlinear perturbations. J. Frankl. Inst. 354 (2017), 4549-4572. DOI | MR 3655782
[20] Zhang, W., Su, H., Zhu, F., Azar, G.: Unknown input observer design for one-sided Lipschitz nonlinear systems. Nonlinear Dyn. 79 (2015), 2, 1469-1479. DOI | MR 3302781
[21] Zhang, Z., Zhang, Z., Zhang, H.: Finite-time stability analysis and stabilization for uncertain continuous-time system with time-varying delay. J. Frankl. Inst. 352 (2015), 1296-1317. DOI | MR 3306527
[22] Zhang, Z., Zhang, Z., Zhang, H., Zheng, B., Karimi, H. R.: Finite-time stability analysis and stabilization for linear discrete-time system with time-varying delay. J. Frankl. Inst. 351 (2014), 3457-3476. DOI | MR 3201042
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