Algorithms for Solving a Unilateral Quadratic Matrix Equation and the Model Updating Problem
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The Schur and doubling methods, which are usually used to solve the algebraic Riccati equation, are generalized to the case of unilateral quadratic matrix equations. The efficiency of the algorithms proposed to solve the unilateral quadratic matrix equation is demonstrated by way of examples. The algorithms are compared with well-known ones. It is shown that the solutions of the unilateral quadratic matrix equation can be used to update model parameters.
Keywordsunilateral quadratic matrix equation linear matrix inequality model updating
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- 1.O. M. Golubentsev and O. M. Drogovoz, “Criteria of aperiodic stability of motion,” Prikl. Mekh., 8, No. 4, 17–23 (1962).Google Scholar
- 2.M. G. Krein, “An introduction to the geometry of indefinite J-spaces and the theory of operators in these spaces,” in: Proc. 2nd Summer Math. School [in Russian], Issue I, Naukova Dumka, Kyiv (1965), pp. 15–92.Google Scholar
- 3.V. B. Larin, “Selecting the parameters of the optimal damper,” in: Proc. 1st Resp. Conf. of Young Mathematicians of Ukraine [in Russian], Inst. Mat. AN USSR, Kyiv (1965), pp. 395–405.Google Scholar
- 4.V. B. Larin, Statistical Vibration-Isolation Problems [in Russian], Naukova Dumka, Kyiv (1974).Google Scholar
- 15.P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox Users Guide, The MathWorks Inc. (1995).Google Scholar
- 18.V. B. Larin, “Optimization of periodic systems with singular weight matrix which defines the quadratic form of control actions,” J. Automat. Inform Sci., 31, No. 6, 27–38 (1999).Google Scholar
- 21.V. B. Larin, “Determination both as stabilizing and antistabilizing solutions of the discrete-time algebraic Riccati equation,” Int. J. Appl. Math. Mech., 3, No. 1, 42–60 (2007).Google Scholar
- 24.Y. Yuan, “An iterative updating method for damped gyroscopic systems,” Int. J. Comput. Math. Sci., 4:2, 63–71 (2010).Google Scholar