Dissipative Approach in Analysis and Synthesis of Control System via Linear Matrix Inequalities

Authors

  • Asep Najmurrokhman Universitas Jenderal Achmad Yani

DOI:

https://doi.org/10.26874/jt.vol7no2.282

Keywords:

dissipative, dissipativity, LMI, solvability condition

Abstract

This paper discusses about application of dissipative concept in dynamical systems for analysis and synthesis of control systems via linear matrix inegualities (LMIs). Motivated by dissipativity concept in mechanical and electrical circuit system, one could employ this concept to check stability and to design a controller of the underlying system. We derive the solvability condition of dissipativity for an output feedback LTI continuous system via LMIs. An algorithm to design such controller that satisfy the dissipativity of the system is also considered.

Author Biography

  • Asep Najmurrokhman, Universitas Jenderal Achmad Yani

    Teknik Elektro

References

(1) J.C. Willems, Dissipative dynamical systems Part I : General Theory, Part II : Linear Systems with guadratic supply rates, Arch. Rational Mechanics and Analysis, vol. 45, no. 5, 1972, pp 321-393.

(2) W.M Grniggs, et. al, A "mixed†small gain and passivity theorem in the frequency domain, System and Control Letters 56 (2007), pp. 596-602.

(3) S. Gupta, Robust Stabilization of Uncertain Systems based on Energy Dissipation Concepts, N4S4 Contractor Report 4713, 1996.

(4) J.A. Moreno, A Separation Property of Dissipative Observers for Nonlinear Systems, in Proc. of the 45th IEEE Conf. on Decision and Control, San Diego, CA, USA, Dec. 13-15, 2006, pp. 1647-1652

(5) G.B. Stain, Analysis of Interconnected Oscillators by Dissipativity Theory, IEEE Trans.Automat. Contr., vol. 52, 2007, pp. 256-270.

(6) S. Lim and J.P. How, Analysis of linear parameter-varying Systems using a non-smooth dissipative systems framework, Int. Jounal of Robust and Nonlinear Control, vol 12, 2002, pp. 1067-1092.

(7) LC Willems, Dissipative Dynamical Systems, European Journal of Control vol. 13, 2007, pp. 134-151.

(8) S. Boyd. et. al., Linear Matrix Inequalities in System and Control Theory, SI4M Studies in Applied Mathematics vol. 15, 1994.

(9) W.M Lu and J C Doyle, H, Control of Nonlinear Systems : A Convex Characterization, IEEE Trans. Automat. Contr., vol. 40, September 1995, pp. 1668-1675.

(10) P. Gahinet and P. Apkarian, A Linear Matrix Inequality Approach to H,, Control, Int. J. Robust Nonlinear Control, vol 4, 1994, pp. 421-428.

(11) A.J. van der Schaft, L2-Gain Analysis of Nonlinear Systems and Nonlinear State Feedback H∞ Control, IEEE Trans. Automat. Contr., vol. 37, no. 6, June, 1992, pp. 770-784.

Additional Files

Published

2020-09-01

How to Cite

Dissipative Approach in Analysis and Synthesis of Control System via Linear Matrix Inequalities. (2020). Jurnal Teknik: Media Pengembangan Ilmu Dan Aplikasi Teknik, 7(2), 62-71. https://doi.org/10.26874/jt.vol7no2.282

Similar Articles

1-10 of 14

You may also start an advanced similarity search for this article.