Abstract
A method was proposed to calculate the anisotropic norm characterizing robustness of the linear discrete-time descriptor systems to random perturbations with uncertain statistical properties. A numerical example was presented.
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Stevens, B.L. and Lewis, F.L., Aircraft Modeling, Dynamics and Control, New York: Wiley, 1991.
Newcomb, R.W., The Semistate Description of Nonlinear Time-Variable Circuits, IEEE Trans. Circuit. Syst, 1981, vol. 28, pp. 62–71.
Newcomb, R.W. and Dziurla, B., Some Circuits and Systems Applications of Semistate Theory, Circuit. Syst. Sig. Process, 1989, vol. 8, pp. 235–260.
Hemami, H. and Wyman, B.F., Modeling and Control of Constrained Dynamic Systems with Application to Biped Locomotion in the Frontal Plane, IEEE Trans. Automat. Control, 1979, vol. 24, pp. 526–535.
Luenberger, A. and Arbel, D.G., Singular Dynamic Leontief Systems, Econometrica, 1977, vol. 45, pp. 991–995.
Campbell, S.L., Singular Systems of Differential Equations, San Francisco: Pitman, 1980.
Campbell, S.L., Singular Systems of Differential Equations II, San Francisco: Pitman, 1982.
Kumar, A. and Daoutidis, P., State-space Realizations of Linear Differential-Algebraic Equation Systems with Control-dependent State Space, IEEE Trans. Automat. Control, 1996, vol. 41, pp. 269–274.
Chistyakov, V.F. and Shcheglova, A.A., Izbrannye glavy teorii algebro-differentsial’nykh sistem (Selected Chapters of the Theory of Algebro-Differential Systems), Novosibirsk: Nauka, 2003.
Boyarintsev, Yu.E., Lineinye i nelineinye algebro-differentsial’nye sistemy (Linear and Nonlinear Algebro-Differential Systems), Vasil’ev, S.N., Ed., Novosibirsk: Nauka, 2000.
Verghese, G.C., Levy, B.C., and Kailath, T., A Generalized State-space for Singular Systems, IEEE Trans. Automat. Control, 1981, vol. 26, pp. 811–831.
Banaszuk, A., Kociecki, M., and Lewis, F.L., Kalman Decomposition for Implicit Linear Systems, IEEE Trans. Automat. Control, 1992, vol. 37, pp. 1509–1514.
Semyonov, A.V., Vladimirov, LC, and Kurdjukov, A.P., Stochastic Approach to H∞-optimization, in Proc. 33rd IEEE Conf. Decision Control, Florida, 1994, pp. 2249–2250.
Vladimirov, LC, Kurdyukov, A.P., and Semenov, A.V., Signal Anisotropy and Entropy of Linear Stationary Systems, Dokl. Ross. Akad. Nauk, 1995, vol. 342, no. 5, pp. 583–585.
Vladimirov, LC, Kurdyukov, A.P., and Semenov, A.V., Stochastic Problem of H∞-optimization, Dokl. Ross. Akad. Nauk, 1995, vol. 343, no. 5, pp. 607–609.
Vladimirov, LC, Kurdjukov, A.P., and Semyonov, A.V., On Computing the Anisotropic Norm of Linear Discrete-time-invariant Systems, in Proc. 13th IFAC World Congr., San-Francisco, 1996, pp. 179–184.
Vladimirov, LC, Kurdjukov, A.P., and Semyonov, A.V., State-space Solution to Anisotropy-Based Stochastic H∞-optimization Problem, in Proc. 13th IFAC World Congr., San-Francisco, 1996, pp. 427–432.
Vladimirov, LC, Kurdyukov, A.P., and Semyonov, A.V., Asymptotics of Anisotropic Norms of Stationary Linear Systems, Autom. Remote Control, 1999, no. 3, part 1, pp. 359–366.
Dai, L., Singular Control Systems, Lecture Notes in Control and Information Sciences, New York: Springer-Verlag, 1989.
Xu, S. and Lam, J., Robust Control and Filtering of Singular Systems, Lecture Notes in Control and Information Sciences, Berlin: Springer-Verlag, 2006.
Gantmakher, F.R., Teoriya matrits (Theory of Matrices), Moscow: Nauka, 1966. Translated into English under the title Theory of Matrices, New York: Chelsea, 1959.
Gray, R.M., Entropy and Information Theory, New York: Springer-Verlag, 1990.
Vladimirov, LC, Diamond, P., and Kloeden, P., Anisotropy-based Robust Performance Analysis of Finite Horizon Linear Discrete Time Varying Systems, Autom. Remote Control, 2006, no. 8, pp. 1265–1282.
Diamond, P., Vladimirov, L, Kurdjukov, A., and Semyonov, A., Anisotropy-based Performance Analysis of Linear Discrete Time Invariant Control Systems, Int. J. Control, 2001, vol. 74, no. 1, pp. 28–42.
Stykel, T., Input-Output Invariants for Descriptor Systems, Calgary: Univ. Calgary, 2003.
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Original Russian Text © A.A. Belov, A.P. Kurdyukov, 2010, published in Avtomatika i Telemekhanika, 2010, No. 6, pp. 51–63.
This work was supported by the Program for Fundamental Research no. 15, the Department of Power Engineering, Machine Building, Mechanics, and Control Processes, Russian Academy of Sciences and the Russian Foundation for Basic Research, project no. 08-08-00567.
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Belov, A.A., Kurdyukov, A.P. Calculation of the anisotropic norm of the descriptor system. Autom Remote Control 71, 1022–1033 (2010). https://doi.org/10.1134/S0005117910060044
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DOI: https://doi.org/10.1134/S0005117910060044