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Keywords:
stochastic stability; composite stochastic system; feedback law; stochastic observer
Summary:
The present paper addresses the problem of the stabilization (in the sense of exponential stability in mean square) of partially linear composite stochastic systems by means of a stochastic observer. We propose sufficient conditions for the existence of a linear feedback law depending on an estimation given by a stochastic Luenberger observer which stabilizes the system at its equilibrium state. The novelty in our approach is that all the state variables but the output can be corrupted by noises whereas in the previous works at least one of the state variable should be unnoisy in order to design an observer.
References:
[1] I.Byrnes, C., Isidori, A.: New results and examples in nonlinear feedback stabilization. Systems Control Lett. 12 (1989), 437-442. DOI  | MR 1005310
[2] Chabour, R., Florchinger, P.: Exponential mean square stability of partially linear stochastic systems. Appl. Math. Lett. 6 (1993), 6, 91-95. DOI  | MR 1348472
[3] Dani, A., Chung, S. J., Hutchison, S.: Observer design for stochastic nonlinear systems via contraction-based incremental stability. IEEE Trans. Automat. Control 60 (2014), 3, 700-714. DOI  | MR 3318397
[4] Ding, D., Han, Q. L., Wang, Z., Ge, X.: Recursive filtering of distributed cyber-physical systems with attack detection. IEEE Trans. Systems Man Cybernet.: Systems 51 (2021), 10, 6466-6476. DOI  | MR 0697005
[5] Ding, D., Wang, Z., Han, Q. L.: Neural-network-based consensus control for multiagent systems with input constraints: The event-triggered case. IEEE Trans. Cybernet. 50 (2020), 8, 3719-3730. DOI 
[6] Ferfera, A., Hammami, M. A.: Stabilization of composite nonlinear systems by a estimated state feedback law. In: Proc. IFAC Symposium on Nonlinear Control System Design (NOLCOS 95), Tahoe City 1995, pp. 697-701.
[7] Florchinger, P.: Stabilization of partially linear stochastic systems via estimated state feedback law. In: Proc. IFAC Symposium on Nonlinear Control System Design (NOLCOS 95), Tahoe City 1995, pp. 753-758.
[8] Florchinger, P.: Global stabilization of composite stochastic systems. Int. J. Comput. Math. Appl. 33 (1997), 6, 127-135. DOI  | MR 1449219
[9] Florchinger, P.: Global stabilization of nonlinear composite stochastic systems. In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 1999, pp. 5036-5037. MR 1449219
[10] Ghanes, M., Leon, J. De, Barbot, J.: Observer design for nonlinear systems under unknown time-varying delays. IEEE Trans. Automat. Control 58 (2013), 1529-1534. DOI  | MR 3065135
[11] Gauthier, J. P., Kupka, I.: Deterministic Observation Theory and Applications. Cambridge University Press, Cambridge 2001. MR 1862985
[12] Hu, X.: On state observers for nonlinear systems. Systems Control Lett. 17 (1991), 465-473. DOI  | MR 1138946
[13] Khasminskii, R. Z.: Stochastic Stability of Differential Equations. Sijthoff and Noordhoff, Alphen aan den Rijn 1980. DOI  | Zbl 1241.60002
[14] Kokotovic, P. V., Sussmann, H. J.: A positive real condition for global stabilization of nonlinear systems. Systems Control Lett. 13 (1989), 125-133. DOI  | MR 1014238
[15] Kou, S. R., Elliott, D. L., Tarn, T. G.: Exponential observers for nonlinear dynamic systems. Inform. Control 29 (1975), 204-216. DOI  | MR 0384227
[16] Luenberger, D. G.: Observing the state of a linear system. IEEE Trans. Military Electron. 8 (1964), 74-80. DOI 
[17] Luenberger, D. G.: An introduction to observers. IEEE Trans. Automat. Control 16 (1971), 596-602. DOI 
[18] Lin, Z., Saberi, A.: Semi-global stabilization of partially linear composite systems via linear dynamic state feedback. In: Proc. 32nd IEEE Conference on Decision and Control, San Antonio 1993, pp. 2538-2543. MR 1302561
[19] Saberi, A., Kokotovic, P. V., Sussmann, H. J.: Global stabilization of partially linear composite systems. SIAM J. Control Optim. 28 (1990), 6, 1491-1503. DOI  | MR 1075215
[20] Sontag, E. D.: Smooth stabilization implies coprime factorization. IEEE Trans. Automat. Control 34 (1989), 435-443. DOI  | MR 0987806
[21] Tarn, T. J., Rasis, Y.: Observers for nonlinear stochastic systems. IEEE Trans. Automat. Control 21 (1976), 4, 441-448. DOI  | MR 0411794
[22] J.Tsinias: Sufficient Lyapunov-like conditions for stabilization. Math. Control Signals Systems 2 (1989), 343-357. DOI  | MR 1015672
[23] Tsinias, J.: Theorem on global stabilization of nonlinear systems by linear feedback. Systems Control Letters 17 (1991), 357-362. DOI  | MR 1136537
[24] Wonham, W. M.: On a matrix Riccati equation of stochastic control. SIAM J. Control Optim. 6 (1968), 4, 681-697. DOI  | MR 0239161
[25] Wu, J., Karimi, H., Shi, P.: Observer-based stabilization of stochastic systems with limited communication. Math. Problems Engrg. 2012 (2012), Article ID 781542, 17 pp. MR 2964997
[26] Zhang, X. M., Han, Q. L., Ge, X., Zhang, B. L.: Delay-variation-dependent criteria on extended dissipativity for discrete-time neural networks with time-varying delay. IEEE Trans. Neural Networks Learning Systems (2021), 1-10. DOI  | MR 3453276
[27] Zhang, X. M., Han, Q. L., Wang, J.: Admissible delay upper bounds for global asymptotic stability of neural networks with time-varying delays. IEEE Trans. Neural Networks Learning Systems 29 (2018), 11, 5319-5329. DOI  | MR 3867847
[28] Zhou, L., Xiao, X., Lu, G.: Observers for a Class of Nonlinear Systems with Time-Delay. Asian J. Control 11 (2009), 688-693. DOI  | MR 2791315
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