Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-14T12:19:20.659Z Has data issue: false hasContentIssue false
  • English
  • Français

Output Feedback Admissible Control for Singular Systems: Delta Operator (Discretised) Approach

Part of:Controllability, observability, and system structure

Published online by Cambridge University Press:  02 May 2017

Xin-zhuang Dong and
Mingqing Xiao
Xin-zhuang Dong
Affiliation:
College of Automation and Electrical Engineering, Qingdao University, Qingdao Shandong 266071, China
Mingqing Xiao*
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, IL 62901, USA
*
*Corresponding author. Email address:mingqingxiao30@gmail.com (M. Xiao)

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Singular systems simultaneously capture the dynamics and algebraic constraints in many practical applications. Output feedback admissible control for singular systems through a delta operator method is considered in this article. Two novel admissibility conditions, derived for the singular delta operator system (SDOS) from a singular continuous system through sampling, can not only produce unified admissibility for both continuous and discrete singular systems but also practical procedures. To solve the problem of output feedback admissible control for the SDOS, an existence condition and design procedure is given for the determination of a physically realisable observer for the state estimation, and then a suitable state-feedback-like admissible controller design based on the observer is developed. All of the conditions presented are necessary and sufficient, involving strict linear matrix inequalities (LMI) with feasible solutions obtained with low computational costs. Numerical examples illustrate our approach.

Keywords

Singular delta operator system (SDOS)admissibilityoutput feedbackstate observerlinear matrix inequalities (LMI)

MSC classification

Secondary:93B07: Observability93B51: Design techniques (robust design, computer-aided design, etc.)93B52: Feedback control

Information

Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 2 , May 2017, pp. 248 - 268
Copyright
Copyright © Global-Science Press 2017 

References

[1] Luenberger, D.G. and Arbel, A., Singular dynamical Leotief systems, Econometrica 5, 991–995 (1997).Google Scholar
[2] Newcomb, R.W., The semistate description of nonlinear time variable circuits, IEEE Trans. Circuits Syst. 28, 62–67 (1981).Google Scholar
[3] Kumar, A. and Daoutidis, P., Feedback control of nonlinear differential-algebraic equation systems, AIChE J. 41, 619–636 (1995).Google Scholar
[4] Dai, L., Singular Control Systems, Lecture Notes in Control and Information Sciences, Springer, Berlin (1989).Google Scholar
[5] Xu, S. and Lam, J., Robust Control and Filtering of Singular Systems, Springer, Berlin (2006).Google Scholar
[6] Lu, R., Su, H., Xue, A. and Chu, J., Robust Control Theory of Singular Systems, Science Press, Beijing (2008).Google Scholar
[7] Duan, G., Analysis and Design of Descriptor Linear Systems, Science Press, Beijing (2012).Google Scholar
[8] Yang, C., Zhang, Q. and Zhou, L., Stability Analysis and Design for Nonlinear Singular Systems, Springer, Berlin (2013).Google Scholar
[9] Wu, Z., Su, H., Shi, P and Chu, J., Analysis and Synthesis of Singular Systems with Time-Delays, Springer, Berlin (2013).Google Scholar
[10] Fridman, E. and Shaked, U., A descriptor system approach to H∞ control of linear time- delay systems, IEEE Trans. Automat. Contr. 47, 253–270 (2002).Google Scholar
[11] Cao, Y. and Lin, Z., A descriptor system approach to robust stability analysis and controller synthesis, IEEE Trans. Automat. Contr. 49, 2081–2084 (2004).Google Scholar
[12] Middleton, R. and Goodwin, G.C., Improved finite word length characteristics in digital control using delta operators, IEEE Trans. Automat. Contr. 31, 1015–1021 (1986).Google Scholar
[13] Goodwin, G.C., Lozano Leal, R., Mayne, D.Q. and Middleton, R.H., Rapproachement between continuous and discrete model reference adaptive control, Automatica 22, 199–207 (1986).Google Scholar
[14] Li, G. and Gevers, M., Comparative study of finite wordlength effects in shift and delta operator parameterisations, IEEE Trans. Automat. Contr. 38, 803–807 (1993).Google Scholar
[15] Wu, J., Li, G., Istepanian, R.H. and Chu, J., Shift and delta operator realisation for digital controllers with finite word length consideration, IEE Proc. - Control Theory and Applications 147, 664–672 (2000).Google Scholar
[16] Li, H., Wu, B., Li, G. and Yang, C., Basic Theory of Delta Operator Control and Robust Control, National Defence Industry Press, Beijing (2005).Google Scholar
[17] Yang, H., Xia, Y. and Shi, P., Observer-based sliding mode control for a class of discrete systems via delta operator approach, J. Franklin Institute 347, 1199–1213 (2010).Google Scholar
[18] Yang, H. and Xia, Y., Low frequency positive real control for delta operator systems, Automatica 48, 1791–1795 (2012).Google Scholar
[19] Yang, H., Xia, Y., Shi, P. and Zhao, L., Analysis and Synthesis of Delta Operator Systems, Springer, Berlin (2012).Google Scholar
[20] Dong, X., Controllability analysis of linear singular delta operator systems, Proc. 12th Int. Conf. Control, Automation, Robotics and Vision, Guangzhou, China, pp. 1199-1204 (2012).Google Scholar
[21] Dong, X., Mao, Q., Tian, W. and Wang, D., Observability analysis of linear singular delta operator systems, Proc. 10th IEEE Int. Conf. Control and Automation, Hangzhou, China, pp. 10-15 (2013).Google Scholar
[22] Dong, X., Admissibility analysis of linear singular systems via a delta operator method, Int. J. Systems Science 45, 2366–2375 (2014).Google Scholar
[23] Dong, X. and Xiao, M., Admissible control of linear singular delta operator systems, Circuits, Systems, Signal Processing 33, 2043–2064 (2014).CrossRefGoogle Scholar
[24] Dong, X., Xiao, M., Wang, Y. and He, W., Observer-based admissible control for singular delta operator systems, Proc. 14th Int. Conf. Control, Automation and Systems, Korea, pp. 1117-1122 (2014).Google Scholar
[25] Dong, X., LMI-based robust admissible control for uncertain singular delta operator systems, Int. J. Systems Sc 46, 2101–2110 (2015).Google Scholar
[26] Dong, X. and Xiao, M., D-admissible hybrid control of a class of singular systems, Nonlinear Analysis: Hybrid Systems 17, 94–110 (2015).Google Scholar
[27] Koenig, D. and Mammar, S., Design of proportional-integral observer for unknown input descriptor systems, IEEE Trans. Automat. Contr. 47, 2057–2062 (2002).Google Scholar
[28] Koenig, D., Observer design for unknown input nonlinear descriptor systems via convex optimisation, IEEE Trans. Automat. Contr. 51, 1047–1052 (2006).CrossRefGoogle Scholar
[29] Lu, G. and Ho, D.W.C., Full-order and reduced-order observers for Lipschitz desriptor systems: the unified LMI approach, IEEE Trans. Circuits and Systems 53, 563–567 (2006).Google Scholar
[30] Wang, Z., Shen, Y., Zhang, X. and Wang, Q., Observer design for discrete-time descriptor systems: an LMI approach, Systems Control Letts. 61, 683–687 (2012).Google Scholar