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The Maximal Solution and Comparison Theorems for the Periodic Discrete-Time Riccati Equation

  • Xiao-Shan Chen (a1)
Abstract
Abstract

Properties and comparison theorems for the maximal solution of the periodic discrete-time Riccati equation are supplemented by an extension of some earlier results and analysis, for the discrete-time Riccati equation to the periodic case.

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*Corresponding author. Email address: chenxs33@163.com (X. S. Chen)
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[1] Benner P., Mehrmann V. and Xu H., Perturbation analysis for the eigenvalue problem of a formal product of matrices, BIT Numer. Math. 42, 143 (2002).
[2] Bolzern P. and Colaneri P., The periodic Lyapunov equation, SIAM J. Matrix Anal. Appl. 9, 499511 (1988).
[3] Bittanti S., Colaneri P. and Nicolao G.D., The difference periodic Riccati equaion for the periodic prediction problem, IEEE Trans. Automat. Control 33, 706712 (1988).
[4] Bittanti S., Colaneri P. and Nicolao G.D., The periodic Riccati equation, in Bittanti S., Laub A. and Willems J.(Eds), The Riccati equation, pp. 172–162, Springer (1991).
[5] Chu E.K.W., Fan H.Y. and Lin W.W., Reachability and observability of periodic descriptor systems, Preprint 2005-1-009, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan (2005).
[6] Chu E.K.W., Fan H.Y. and Lin W.W., Projected generalized discrete-time periodic Lyapunov equaitons and balanced realization of periodic decriptor systems, SIAM J. Matrix Anal. Appl. 29, 9821006 (2007).
[7] Granat R., Kågström B., Direct eigenvalue reordering in a product of matrices in extended periodic Schur form, SIAM J. Matrix Anal. Appl. 28, 285300 (2006).
[8] Horn R.A. and Johnson C.R., Topics in Matrix Analysis, Cambridge University Press (1991).
[9] Lancaster P. and Rodman L., Algebraic Riccati Equations, Oxford University Press (1995).
[10] Hench J.J. and Laub A.J., Numerical solution of the discrete-time periodic Riccati equation, IEEE Trans. Auto. Control 39, 11971210 (1994).
[11] Kuo Y.C., Lin W.W. and Xu S.F., Regularization of linear discrete-time perioidc descriptor systems by derivative and proportional state feedback, SIAM J. Matrix Anal. Appl. 25, 10461073 (2004).
[12] Lainiot D., Assimak N., and Katsikas S., New doubling algorithm for the discrete periodic Riccati equation, Applied Math. Comput. 60, 265283 (1994).
[13] Lin W.W., Van Dooren P. and Xu Q.F., Equivalent characterizations of periodical invariant sub-spaces, NCTS Preprints Series, Taiwan, http://www.math.cts.nthu.edu.tw/publish (1998).
[14] Lin W.W. and Sun J.G., Perturbation analysis for eigenproblem of periodic matrix pairs, Linear Algebra Appl. 337, 157187 (2001).
[15] Lin W.W. and Sun J.G., Perturbation analysis of the periodic discrete-time algebraic Riccati equation, SIAM J. Matrix Anal. Appl. 24, 411438 (2002).
[16] Nishimura T. and Kano H., Algebraic solution of Riccati equations in discrete, periodically time-varying systems with detectability and stabilisability (in Japanese), Trans. SICE 14, 486493 (1978).
[17] Ran A.C.M. and Vreugdenhil R., Existence and comparison theorems for algebraic Riccati equaitons for continuous- and discrete-time systems, Linear Algebra Appl. 99, 6383 (1988).
[18] Sun J.G., Backward perturbation analysis of the periodic discrete-time algebraic Riccati equation, SIAM J. Matrix Anal. Appl. 26, 119 (2004).
[19] de Souza C.E., Existence conditions and properties for the maximal periodic solution of periodic Riccati difference equations, Int. J. Control 50, 731742 (1989).
[20] de Souza C.E., Periodic strong solution for the optimal filtering problem of linear discrete-time periodic systems, IEEE Trans. Automat. Contr. 36, 333337 (1991).
[21] Varga A., On solving periodic Riccati equations, Numer. Linear Algebra Appl. 15, 809835 (2008).
[22] Wimmer H.K., Monotonicity and maximality of solutions of discrete-time algebraic Riccati equations, J. Math. Syst. Estim. Control 2, 219235 (1992).
[23] Fan H.Y., Lin W.W. and Xu S.F., Pole assignment in decriptor periodic systems, Science in China Ser. A Mathematics 48, 13091332 (2005).
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East Asian Journal on Applied Mathematics
  • ISSN: 2079-7362
  • EISSN: 2079-7370
  • URL: /core/journals/east-asian-journal-on-applied-mathematics
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