Abstract
This paper considers the design of output tracking and feedback controllers for nonlinear stochastic systems. The system status cannot be measured. The studied system contains nonlinear state functions, noise disturbances and time delays. We use the free weight matrix method to avoid the conservatism caused by the use of model transformation or cross-term bounded techniques. Based on the Lyapunov-Krasovskii functional method, we propose an output tracking and feedback controller design method based on linear matrix inequality (LMI). Numerical examples show the validity of the obtained results.
Similar content being viewed by others
References
Bucy R.S., Joseph P.D.: Filtering for Stochastic Processes with Applications to Guidance[M]. Interscience, New York (1968)
Gelb A.: Applied Optimal Estimation[M]. Cambridge University Press, Cambridge (1974)
Hsiao, F., Pan, S.: Robust kalman filter synthesis for uncertain multiple time-delay stochastic systems [J]. J. Dynam. Syst. Meas. Control 118, 803–808 (1996)
Hsieh, C., Skelton, R.E.: All covariance vontrollers for linear discrete time systems [J]. IEEE Trans. Autom. Control 35, 908–915 (1990)
Ito, K., Rozovskii, B.: Approximation of the kushner equation for nonlinear filtering [J]. Soc. Indust. Appl. Math. J. Control. Opt. 38, 893–915 (2000)
Jazwinski A.H.: Stochastic Processes and Filtering Theory[M]. Academic Press, New York (1970)
Wang, Z., Burnham, K.J.: Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation [J]. IEEE Trans. Signal Process. 49, 794–804 (2001)
Shaikhet, L.: Stability of stochastic hereditary systems with markov switching [J]. Theory Stochastic Process. 2, 180–184 (1996)
Willems, J.L., Willems, J.C.: Feedback stabilizability for stochastic systems with state and control dependent noise [J]. Automatica 12, 343–357 (1976)
Basin, M.V., Rodkina, A.E.: On delay-dependent stability for a class of nonlinear stochastic systems with multiple state delays [J]. Nonlinear Anal. Theory Meth. Appl. 68, 2147–2157 (2008)
Huang, L., Deng, F.: Robust exponential stabilization of stochastic largescale delay systems [J]. In: Proceedings of 2007 IEEE international conference on control and automation, pp 107–112 (2007)
Luenberger, D.G.: Observers for multi-variable systems [J]. IEEE Trans. Auto. Con. 11, 190–197 (1996)
He, Y., Wang, Q.G., Lin, C., et al.: Delay-range-dependent stability for systems with timevarying delay [J]. Automatica 43, 371–376 (2007)
Li, H., Chen, B., Zhou, Q., et al.: Delay dependent robust stability for stochastic time-delay systems with polytopic uncertainties [J]. Int. J. Robust Nonlinear Control 18, 1482–1492 (2008)
Li, H., Chen, B., Zhou, Q., et al.: A delay dependent approach to robust\(h_{\infty }\) control for uncertain stochastic systems with state and input delays [J]. Circ. Syst. Signal Process. 28, 169–183 (2009)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Li, Y., Wang, Y. Output Tracking and Feedback Controller Design for Nonlinear Stochastic Time-Delay System. Int J Theor Phys 60, 2499–2510 (2021). https://doi.org/10.1007/s10773-020-04638-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-020-04638-3