State Estimation for a Class of Singular Systems Using Shifted Legendre Polynomials

Majlesi Journal of Electrical Engineering

مقاله 7، دوره 10، شماره 3، آذر 2016، صفحه 1-7   

نوع مقاله: Review Article

نویسندگان

Zahra Razavinasab^* ؛ Mohammad Ali Vali؛ Mahmoud Samavat

Shahid Bahonar University of Kerman

چکیده

For linear time-invariant continuous-time singular systems, two new simple approaches, the Kronecker method and the recursive method, are developed in order to estimate the states from the system input-output information via shifted Legendre polynomials (SLP) and a simple observer in the descriptor form. Sufficient conditions for the existence of the present observer are given. The two methods simplify the system of state equations into the solution of a set of linear algebraic equations. Furthermore, the proposed algorithms can be easily implemented in a digital computer and the solutions can be obtained for any length of time. Further, these approaches include the filtering and the smoothing effect which can reduce the influence of zero-mean measurement noise on estimation. Simulation results of a given numerical example demonstrate the effect of the proposed approaches.

کلیدواژه‌ها

Descriptor observer؛ en؛ Shifted Legendre polynomials؛ Singular systems؛ State estimation

مراجع

J. D. Cobb, “Controllability, observability and duality in singular systems,” IEEE Trans. Autom. Control, vol. 12, pp. 1076–1082, 1984.

L. Dai, “Singular Control Systems”, Berlin, Springer, 1989.

M. Alma, M. Darouach, “Adaptive observers design for a class of linear descriptor systems,” Automatica, vol.50, pp. 578-583, 2014.

Z. Razavinasab, M. Samavat, M. A. Vali, “Analysis of singular transistor circuits using the orthogonal functions”, Far East J. of Applied Mathematics, 61, pp. 117-135, 2012.

M. Hou, P.C. Muller, “Design of a class of Luenberger observers for descriptor systems”, IEEE Trans. Autom. Control, vol. 40, pp. 133–136, 1995.

M. Darouac, M. Boutayeb, “Design of observers for descriptor systems”, IEEE Trans. Autom. Control, vol. 40, pp. 1323–1327, 1995.

A. G. Wu, G. R. Duan, “IP observer design for descriptor linear systems”, IEEE Trans. Circuits Syst. II, vol. 36, pp. 1423–1431, 2006.

M. Darouach, “Functional observers for linear descriptor systems”, 17th Mediterranean Conf. Control & Automation, Greece, Makedonia Palace, Thessaloniki, June 24-26, pp. 1535-1539, 2009.

B. M. Mohan, S. K. Kar, “State estimation using Block-Pulse functions”, India Conf., Annual IEEE., India, Kanpur, 27 January, pp. 280-285, 2009.

J. H. Chou, I. R. Horng, “State estimation using continuous orthogonal functions”, Int. J. Systems Sci., vol. 17, pp. 1261-1267, 1986.

B. M. Mohan, S. K. Kar, “State Estimation using Shifted Legendre Polynomials”, the Third int. Conf. Industrial and Information Systems, IEEE Region 10, India, Kharagpur, December 8-10, pp. 1-6, 2008.

Z. Razavinasab, M. A. Vali, M., Samavat, “Wavelet analysis of linear optimal control systems incorporating observers”, Int. J. Innovative Computing, Information and Control, vol. 8, pp. 3215-3222, 2012.

K. B. Datta, B. M. Mohan, “Orthogonal Functions in Systems and Control”, World Scientific, 1995.

M. Zasadzinski, M. Darouach, “State estimation for a class of singular systems”, Int. J. Systems Sci., vol. 23, pp. 517-530, 1992.

M. Darouach, M. Zasadzinski, D. Mehdi, “State estimation of stochastic singular linear systems”, Int. J. Systems Sci., vol. 24, pp. 345-354, 1993.

Z. Gao, D., Ho, “State/Noise Estimator for Descriptor Systems With Application to Sensor Fault Diagnosis”, IEEE Trans. On Signal Proc., vol. 54, pp. 1316-1326, 2006.

L. Elizabeth, L. Yip, R. F., Sincovec, “Solvability, controllability, and observability of continuous descriptor systems”, IEEE Trans. Autom. Control, vol. 26s, pp.702-706, 1981.

J. W. Brewer,. “Kronecker products and matrix calculus in system theory”, IEEE Trans. on Circuits and Systems, cas-25, (9), pp. 772-781, 1978.