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State controllability computation technique for linear time‐varying systems by using Taylor series approximation
Author(s) -
Aksoy S.
Publication year - 2009
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.1066
Subject(s) - controllability , taylor series , gramian matrix , mathematics , polynomial matrix , matrix (chemical analysis) , polynomial , matrix polynomial , matrix exponential , computation , lyapunov function , constant (computer programming) , characteristic polynomial , differential equation , algorithm , mathematical analysis , computer science , nonlinear system , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , composite material , programming language
This article presents a technique to determine the controllability Grammian matrix (CGM) for linear time‐varying systems by using truncated Taylor polynomial vector and the operational matrix of integration. An important property of this algorithm is that it starts by integrating the Lyapunov differential matrix equation in terms of the CGM. However, the algorithm does not use the mathematical integration processes actually, but uses the truncated Taylor polynomial vector and the operational matrix of integration. Thus, the problem is reduced to solving a linear set of algebraic equations with constant coefficients consisting of the Taylor polynomial constant coefficients of each of the CGM elements. Numerical results and error curves are given to illustrate the improvements achieved by the proposed algorithm. Copyright © 2008 John Wiley & Sons, Ltd.