Abstract
This paper considers some synthesis issues for SISO LTI systems. It is shown that direct application of universal methods (such as the two-Riccati approach or the LMI technique) appears impossible in degenerate situations without noisy measurements.
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References
Doyle, J., Francis, B., and Tannenbaum, A., Feedback Control Theory, New York: Macmillan, 1992.
Bhattacharyya, S., Datta, A., and Keel, L., Linear Control Theory: Structure, Robustness and Optimization,Boca Raton: CRC Press, 2009.
Kwakernaak, H., H 2-Optimization—Theory and Applications to Robust Control Design, Annu. Rev.Contr., 2002, vol. 26, no. 1, pp. 45–56.
Meinsma, G., On the Standard H 2-Problem, Proc. Third IFAC Symposium on Robust Control Design,Prague, June 21–23, 2000.
Barabanov, A.E. and Pervozvanskii, A.A., Optimization by Frequency-Uniform Criteria (H-Theory),Autom. Remote Control, 1992, vol. 53, no. 9, part 1, pp. 1301–1327.
Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.
Veremey, E.I., The Spectral Representation of Optimal Solutions to Mean Square Synthesis Problems,Sist. Upravlen. Inform. Tekhn., 2012, vol. 49, no. 3.1, pp. 124–128.
Veremey, E.I., Spectral Approach to Optimization of Control Systems According to the Norms of theSpaces H2 and H∝, Vestn. S.-Peterb. Univ., 2004, ser. 10, no. 1, pp. 48–59.
Veremey, E.I., Optimization Approach to Modeling and Development of Information and Control Systems,Prikl. Inform., 2012, vol. 42, no. 6, pp. 31–41.
Veremey, E.I., Algorithms for Solving a Class of Problems of H8-Optimization of Control Systems,J. Comput. Syst. Sci. Int., 2011, vol. 50, no. 3, pp. 403–412.
Veremey, E.I. and Petrov, Yu.P., A Synthesis Method of Optimal Controllers with the Feature of Realizability,in Matematicheskie metody issledovaniya upravlyaemykh mekhanicheskikh sistem (MathematicalMethods for Analysis of Controlled Mechanical Systems), Leningrad: Leningr. Gos. Univ., 1982,pp. 24–31.
Veremey, E. and Sotnikova, M., Spectral Approach to H∝-Optimal SISO Synthesis Problem, WSEASTrans. Syst. Control, 2014, vol. 9, art. no. 43, pp. 415–424.
Provotorov, V.V. and Volkova, A.S., Nachal’no-kraevye zadachi s raspredelennymi parametrami na grafe(Initial Boundary Problems with Distributed Parameters on a Graph), Voronezh: Nauchnaya Kniga,2014.
Podvalny, S.L. and Vasiljev, E.M., A Multi-alternative Approach to Control in Open Systems: Origins,Current State and Future Prospects, Upravlen. Bol’sh. Sist., 2014, no. 48, pp. 6–58.
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Original Russian Text © E.I. Veremey, V.V. Eremeev, N.A. Zhabko, S.V. Pogozhev, 2014, published in Sistemy Upravleniya i Informatsionnye Tekhnologii, 2014, No. 3.1, pp. 219–224.
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Veremey, E.I., Eremeev, V.V., Zhabko, N.A. et al. Degenerate problems of H-optimization for SISO LTI systems and realizability issues. Autom Remote Control 76, 1094–1100 (2015). https://doi.org/10.1134/S0005117915060132
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DOI: https://doi.org/10.1134/S0005117915060132