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Eigenvalue Assignment Of Discrete-Time Linear Systems With State And Input Time-Delays | ||
| AUT Journal of Modeling and Simulation | ||
| مقاله 3، دوره 45، شماره 2، بهمن 2013، صفحه 23-30 اصل مقاله (476.9 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/miscj.2015.526 | ||
| نویسندگان | ||
| H. A. Tehrani* 1؛ N. Ramroodi2 | ||
| 1Assistant Professor, Department of Mathematics, University of Shahrood, Shahrood, Iran | ||
| 2MSc Student, Department of Mathematics, University of Shahrood, Shahrood, Iran | ||
| چکیده | ||
| Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper a new method for eigenvalue assignment of discrete-time linear systems with state and input time-delays by static output feedback matrix is presented. The main result is an iterative method that only requires linear equations to be solved at each iteration. In this scheme, first a linear delayed system by defining an augmented vector is changed to standard form, then output feedback matrix K is calculated by inverse eigenvalue problem. We investigate all types of delays in the states, inputs or both for discrete – time linear systems. A simple algorithm and an illustrative example are presented to show the advantages of this new technique. | ||
| کلیدواژهها | ||
| Eigenvalue assignment؛ Inverse eigenvalue problem؛ Output feedback؛ Time-delay system | ||
| عنوان مقاله [English] | ||
| Eigenvalue Assignment Of Discrete-Time Linear Systems With State And Input Time-Delays | ||
| نویسندگان [English] | ||
| H. A. Tehrani1؛ N. Ramroodi2 | ||
| 1Assistant Professor, Department of Mathematics, University of Shahrood, Shahrood, Iran | ||
| 2MSc Student, Department of Mathematics, University of Shahrood, Shahrood, Iran | ||
| چکیده [English] | ||
| Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper a new method for eigenvalue assignment of discrete-time linear systems with state and input time-delays by static output feedback matrix is presented. The main result is an iterative method that only requires linear equations to be solved at each iteration. In this scheme, first a linear delayed system by defining an augmented vector is changed to standard form, then output feedback matrix K is calculated by inverse eigenvalue problem. We investigate all types of delays in the states, inputs or both for discrete – time linear systems. A simple algorithm and an illustrative example are presented to show the advantages of this new technique. | ||
| کلیدواژهها [English] | ||
| Eigenvalue assignment, Inverse eigenvalue problem, Output feedback, Time-delay system | ||
| مراجع | ||
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[1] H. Ahsani Tehran, “Localization of Eigenvalues in Small Specified Regions of Complex Plane by State Feedback Matrix,” J. Sci. Islam. Repub. Iran, vol 25(2), pp. 157 – 164. [2] M.T. Chu, “Inverse eigenvalue problems,” SIAM, vol 40, pp. 1-39, 1998. [3] Y. Dong and J. Wei, “Output feedback stabilization of nonlinear discrete-time systems with time-delay,” Advances in Difference Equations, vol 73, pp. 1-11,2012. [4] R. Dorf and R.H. Bishop, Modern control system,11th Edition, Prentice Hall 2007. [5] G.H. Golub and C.F. Van Loan, Matrix Computations, 4th Edition, The Johns Hopkins University Press, Baltimore 2013. [6] S.M. Karbassi and D.J. Bell “Parametric timeoptimal control of linear discrete-time systems by state feedback-Part 1: Regular Kronecker invariants,” International Journal of Control, vol. 57, pp. 817-830, 1993. [7] S.M. Karbassi and F. Saadatjou, “A parametric approach for eigenvalue assignment by static output feedback,” Journal of the Franklin Institute, vol. 346,pp. 289-300, 2009. [8] S.M. Karbassi and H.A. Tehrani, “Parameterizations of the state feedback controllers for linear multivariable systems,” Computers and Mathematics with Applications, vol. 44, pp. 1057-1065, 2002. [9] R.W. Koepcke, “On the control of linear systems with pure time-delay,” Trans. ASME Journal of Basic Engineering, vol. 87, pp. 74-80, 1965. [10] F. Kurzweil, “The control of multivariable processes in the presence of the pure transport delays,” IEEE Trans. Automatic Control, vol. 8, pp. 27- 35, 1963. [11] N. Li, “An iterative method for pole assignment,”Linear Algebra and Its applications, vol. 23, pp. 77- 102, 2001. [12] N. Li, “An inverse eigenvalue problem and feedback control,” proceedings of the 4th Biennial engineering mathematics and applications conference, vol. 124, pp. 183-186, 2000. [13] X. Li and H. Gao, “A new model transformation of discrete-time systems with time-varying delay and its application to stability analysis,” IEEE Transactions on Automatic Control, vol. 56, no. 9, pp. 2172–2178, 2011. [14] S.M. Modarres and S.M. Karbassi, “Time-optimal control of discrete time linear systems with state and input time-delays,” International Journal of Innovative Computing, Information and Control,vol. 5, no. 9, pp. 2619-2625, 2009. [15] Y. Xia and G. Liu and P. Shi and D. Rees and E. Thomas, “New stability and stabilization conditions for systems with time-delay,” International Journal of Systems Science, vol. 38, no. 1, pp. 17–24, 2007. | ||
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