Dissipative Control of Singular Systems by Proportional Plus Derivative State Feedback

Abstract:

This article deals with the problem of dissipative control synthesis for a class of descriptor systems with uncertainties in the derivative matrix. Attention is focused on the design of a proportional plus derivative (PD) state feedback, which guarantees that the closed-loop system is robustly stable and strict dissipative. Firstly, a sufficient condition for the closed-loop system is robustly stable and strict dissipative is presented by using a simple idea of changing the problem to the corresponding problem of an augmented uncertain system. Then, a PD controller is constructed by solving LMIs. Finally, a numerical example is given to demonstrate that the proposed method is effective.

• Periodical: Applied Mechanics and Materials (Volumes 246-247)
• Pages: 826-831
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.246-247.826
• Online since: December 2012
• Authors: Shuang Yun Xing, Xin Jing, Yang Cao
• Keywords: Dissipative Control, LMI, Proportional Plus Derivative State (PD) Feedback, Uncertain Singular System

References

[1] Dai, L., Singular Control Systems, Berlin: Springer-Verlag, (1989).

[2] Xu, S., Lam, L., Robust Control and Filtering of Singular Systems, Berlin: Springer-Verlag, (2006).

[3] Ren, J., Zhang Q., Positive real control for descriptor systems with uncertainties in the derivative matrix via a proportional plus derivative feedback. International Journal of Systems Science, Vol. 42, no. 1, 2011, pp.1-11.

DOI: 10.1080/00207721.2011.602481

[4] Xu, S., Yang C., An algebraic approach to the robust stability analysis and robust stabilization of uncertain singular systems. International Journal of Systems Science, Vol. 31, no. 1, 2000 pp.55-61.

DOI: 10.1080/002077200291451

[5] Hill D., Moylan P., The stability of nonlinear dissipative systems. IEEE Trans on Automatic Control. Vol. 21, No. 5, 1976, pp.708-711.

DOI: 10.1109/tac.1976.1101352

[6] Willems J., Dissipative dynamical systems: Part 1. General theory, Archive for Rational Mechanics and Analysis, vol. 45, no. 5, 1972, pp.321-351.

DOI: 10.1007/bf00276493

[7] Dong, X., Robust strictly dissipative control for discrete singular systems, IET Control Theory and Applications, Vol. 1 no. 4, 2007, pp.1060-1067.

DOI: 10.1049/iet-cta:20060173

[8] Yang L., Zhang Q., Robust impulse dissipative control of singular systems with uncertainties. Acta Automatica Sinica, vol33, no. 5, 2007, pp.554-556.

DOI: 10.1360/aas-007-0554

[9] Su X., Robust dissipative control for time-delay bilinear singular systems with uncertainties, Control and Decision, vol. 27, no. 4, 2012, pp.623-626.

[10] Nataša A, K., Dissipativity theory for singular systems. Part I: Continuous-time case, Proceedings of the 44th IEEE Conference on Decision and Control, vol. 2005, 2005, pp.4090-4095.

DOI: 10.1109/cdc.2005.1583061

[11] Feng Z., Lam, L. and Gao H., α-Dissipativity analysis of singular time-delay systems, Automatica, vol. 47, no. 11, 2011, pp.2548-2552.

DOI: 10.1016/j.automatica.2011.06.025

[12] Wu Z., Park J., and Su H., Dissipativity analysis for singular systems with time-varying delays, Applied Mathematics and Computation, vol. 218, no. 8, 2011, pp.4605-4613.

DOI: 10.1016/j.amc.2011.10.044