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Algorithm for solution of equations PA+A\(^T\)P=-Q and M\(^T\)PM-P=-Q resulting in Lyapunov stability analysis of linear systems. (English) Zbl 0274.93040
MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C05 Linear systems in control theory
65H10 Numerical computation of solutions to systems of equations
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References:
[1] Katsuhiko Ogata: State Space Analysis of Control Systems. Prentice Hall, London 1967 · Zbl 0869.93002
[2] Kotek Z., Štecha Jan: Teorie optimálního řízení. (Theory of Optimal Control). Lecture Notes. Praha 1971.
[3] Kleinmann D. L.: On an Iterative Technique for Riccati Equation Computations. Trans. IEEE on Aut. Control AC-13 (Feb. 1968), 1, 114-115.
[4] Chen C. F., Shieh L. S.: A Note on Expanding \(PA + A^{T} P = - Q\). Trans IEEE on Aut. Control AC-13 (Feb. 1968), 1, 122-124.
[5] Sarma I. G., Pai M. A.: A Note on the Lyapunov Matrix Equation for Linear Discrete System. Trans. IEEE on Aut. Control AC-13 (Feb. 1968), 1, 119-121.
[6] Bellmann R.: Introduction to Matrix Analysis. McGraw-Hill, New York 1960.
[7] Dorato P., Lewis A. H.: Optimal Linear Regulators. The Discrete Time Case. Trans. IEEE on Aut. Control AC-16 (Dec. 1971), 6, 613-621.
[8] Fink M., Štecha J.: Linear Optimal Control System with Incomplete Information about State of System. Kybernetika 7 (1971), 6, 467-491. · Zbl 0266.49020 · eudml:28835
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