## Abstract and Applied Analysis

### Nonfragile Gain-Scheduled Control for Discrete-Time Stochastic Systems with Randomly Occurring Sensor Saturations

#### Abstract

This paper is devoted to tackling the control problem for a class of discrete-time stochastic systems with randomly occurring sensor saturations. The considered sensor saturation phenomenon is assumed to occur in a random way based on the time-varying Bernoulli distribution with measurable probability in real time. The aim of the paper is to design a nonfragile gain-scheduled controller with probability-dependent gains which can be achieved by solving a convex optimization problem via semidefinite programming method. Subsequently, a new kind of probability-dependent Lyapunov functional is proposed in order to derive the controller with less conservatism. Finally, an illustrative example will demonstrate the effectiveness of our designed procedures.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 629621, 10 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393447708

Digital Object Identifier
doi:10.1155/2013/629621

Mathematical Reviews number (MathSciNet)
MR3081612

Zentralblatt MATH identifier
07095185

#### Citation

Li, Wangyan; Wei, Guoliang; Karimi, Hamid Reza; Liu, Xiaohui. Nonfragile Gain-Scheduled Control for Discrete-Time Stochastic Systems with Randomly Occurring Sensor Saturations. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 629621, 10 pages. doi:10.1155/2013/629621. https://projecteuclid.org/euclid.aaa/1393447708

#### References

• D. Ding, Z. Wang, B. Shen, and H. Shu, “${H}_{\infty }$ state estimation for discrete-time complex networks with randomly occurring sensor saturations and randomly varying sensor delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 5, pp. 725–736, 2012.
• J. Hu, Z. Wang, H. Gao, and L. K. Stergioulas, “Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occurring uncertainties and randomly occurring nonlinearities,” IEEE Transactions on Industrial Electronics, vol. 59, no. 7, pp. 3008–3015, 2012.
• J. Hu, Z. Wang, H. Gao, and L. K. Stergioulas, “Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements,” Automatica, vol. 48, no. 9, pp. 2007–2015, 2012.
• J. Hu, Z. Wang, Y. Niu, and L. K. Stergioulas, “${H}_{\infty }$ sliding mode observer design for a class of nonlinear discrete time-delay systems: a delay-fractioning approach,” International Journal of Robust and Nonlinear Control, vol. 22, no. 16, pp. 1806–1826, 2012.
• J. Hu, Z. Wang, B. Shen, and H. Gao, “Gain-constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays,” IEEE Transactions on Signal Processing, vol. 61, no. 5, pp. 1230–1238, 2013.
• J. Hu, Z. Wang, B. Shen, and H. Gao, “Quantized recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements,” International Journal of Control, vol. 86, no. 4, pp. 650–663, 2013.
• L. Li and Y. Jia, “Non-fragile dynamic output feedback control for linear systems with time-varying delay,” IET Control Theory & Applications, vol. 3, no. 8, pp. 995–1005, 2009.
• W. Li, G. Wei, and L. Wang, “Probability-dependent static output feedback control for discrete-time nonlinear stochastic systems with missing measurements,” Mathematical Problems in Engineering, vol. 2012, Article ID 696742, 15 pages, 2012.
• B. Shen, Z. Wang, J. Liang, and Y. Liu, “Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: a survey,” Mathematical Problems in Engineering, vol. 2012, Article ID 530759, 16 pages, 2012.
• H. Shu and G. Wei, “${H}_{\infty }$ analysis of nonlinear stochastic time-delay systems,” Chaos, Solitons & Fractals, vol. 26, no. 2, pp. 637–647, 2005.
• H. Shu, Z. Wang, and Z. Lü, “Global asymptotic stability of uncertain stochastic bi-directional associative memory networks with discrete and distributed delays,” Mathematics and Computers in Simulation, vol. 80, no. 3, pp. 490–505, 2009.
• Z. Wang, B. Shen, and X. Liu, “${H}_{\infty }$ filtering with randomly occurring sensor saturations and missing measurements,” Automatica, vol. 48, no. 3, pp. 556–562, 2012.
• Z. Wang, F. Yang, D. W. C. Ho, and X. Liu, “Robust ${H}_{\infty }$ filtering for stochastic time-delay systems with missing measurements,” IEEE Transactions on Signal Processing, vol. 54, no. 7, pp. 2579–2587, 2006.
• G. Wei, Z. Wang, and B. Shen, “Probability-dependent gain-scheduled filtering for stochastic systems with missing measurements,” IEEE Transactions on Circuits and Systems II, vol. 58, no. 11, pp. 753–757, 2011.
• G. Wei, Z. Wang, and B. Shen, “Probability-dependent gain-scheduled control for discrete stochastic delayed systems with randomly occurring nonlinearities,” International Journal of Robust and Nonlinear Control, vol. 23, no. 7, pp. 815–826, 2013.
• F. Yang, Z. Wang, Y. S. Hung, and M. Gani, “${H}_{\infty }$ control for networked systems with random communication delays,” IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 511–518, 2006.
• P. Apkarian and R. J. Adams, “Advanced gain-scheduling techniques for uncertain systems,” IEEE Transactions on Control Systems Technology, vol. 6, no. 1, pp. 21–32, 1998.
• Y.-Y. Cao, Z. Lin, and Y. Shamash, “Set invariance analysis and gain-scheduling control for LPV systems subject to actuator saturation,” Systems & Control Letters, vol. 46, no. 2, pp. 137–151, 2002.
• W. J. Rugh and J. S. Shamma, “Research on gain scheduling,” Automatica, vol. 36, no. 10, pp. 1401–1425, 2000.
• J. H. Park, “Robust non-fragile control for uncertain discrete-delay large-scale systems with a class of controller gain variations,” Applied Mathematics and Computation, vol. 149, no. 1, pp. 147–164, 2004.
• D. Peter, “Non-fragile controller design: an overview,” in Proceedings of the American Control Conference, vol. 5, pp. 2829–2831, 1998.
• G.-H. Yang and W.-W. Che, “Non-fragile ${H}_{\infty }$ filter design for linear continuous-time systems,” Automatica, vol. 44, no. 11, pp. 2849–2856, 2008.
• Y. Cao, J. Lam, and Y. Sun, “Static output feedback stabiliztion: an LMI approach,” Automatica, vol. 34, no. 12, pp. 1641–1645, 1998.
• J. C. Geromel, C. C. de Souza, and R. E. Skelton, “Static output feedback controllers: stability and convexity,” IEEE Transactions on Automatic Control, vol. 43, no. 1, pp. 120–125, 1998.
• I. N. Kar, “Design of static output feedback controller for uncertain systems,” Automatica, vol. 35, no. 1, pp. 169–175, 1999.
• J. Qiu, G. Feng, and H. Gao, “Fuzzy-model-based piecewise ${H}_{\infty }$ static-output-feedback controller design for networked non-linear systems,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 5, pp. 919–934, 2010.
• V. L. Syrmos, C. T. Abdallah, P. Dorato, and K. Grigoriadis, “Static output feedback–-a survey,” Automatica, vol. 33, no. 2, pp. 125–137, 1997.
• S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory,, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 1994.