Dissipative dynamical systems. II: Linear systems with quadratic supply rates. (English) Zbl 0252.93003


93A10 General systems
70Gxx General models, approaches, and methods in mechanics of particles and systems
94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
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[1] Brockett, R. W., Finite Dimensional Linear Systems. New York: Wiley 1970. · Zbl 0216.27401
[2] Kalman, R. E., P. L. Falb, & M. A. Arbib, Topics in Mathematical System Theory. New York: McGraw-Hill 1969. · Zbl 0231.49001
[3] Willems, J. C., & S. K. Mitter, Controllability, observability, pole allocation, and state reconstruction. IEEE Transactions on Automatic Control AC-16, 582-595, December (1971). (Special issue on the Linear-Quadratic-Gaussian Problem). · doi:10.1109/TAC.1971.1099819
[4] Silverman, L. M., Realization of linear dynamical systems, ibid. IEEE Transactions on Automatic Control AC-16, pp. 554-567.
[5] Youla, D. C., L. J. Castriota, & H. J. Carlin, Bounded real scattering matrices and the foundations of linear passive network theory. Trans. IRE Circuit Theory CT-4, 102-124 (1959).
[6] Meixner, J., On the theory of linear passive systems. Arch. Rational Mech. Anal. 17, 278-296 (1964). · Zbl 0173.43205 · doi:10.1007/BF00282291
[7] Willems, J. C., The generation of Lyapunov functions for input-output stable systems. SIAM J. Control 9, 105-134 (1971). · Zbl 0224.93029 · doi:10.1137/0309009
[8] Willems, J. C., Least squares stationary optimal control and the algebraic Riccati equation. IEEE Transactions on Automatic Control AC-16, 621-634, December (1971). (Special issue on the Linear-Quadratic-Gaussian Problem).
[9] Kleinman, D. L., On an iterative technique for Riccati equation computations. IEEE Transactions on Automatic Control AC-13, 114-115 (1968). · doi:10.1109/TAC.1968.1098829
[10] Mårtensson, K., On the matrix Riccati equation. Information Sciences 3, 17-49 (1971). · Zbl 0206.45602 · doi:10.1016/S0020-0255(71)80020-8
[11] Haynsworth, E. V., Determination of the inertia of a partitioned Hermitian matrix. Linear Algebra and Its Applications 1, 73-81 (1968). · Zbl 0155.06304 · doi:10.1016/0024-3795(68)90050-5
[12] Kalman, R. E., Lyapunov functions for the problem of Lur’e in automatic control. Proc. Nat. Acad. Sci. U.S.A. 49, 201-205 (1963). · Zbl 0113.07701 · doi:10.1073/pnas.49.2.201
[13] Yacubovich, V. A., Absolute stability of nonlinear control in critical cases, I and II. Automation and Remote Control 24, 273-282 (1963) and 655-668 (1964).
[14] Popov, V. M., Hyperstability and optimality of automatic systems with several control functions. Rev. Roumaine Sci. Tech. Electrotechn. et Energ. 9, 629-630 (1964).
[15] Kalman, R. E., On a New Characterization of Linear Passive Systems. Proc. of the First Allerton Conference on Circuit and System Theory, Monticello, Ill., pp. 456-470 (1963).
[16] Youla, D. C., & P. Tissi, N-port synthesis via reactance extraction-Part I. 1966 IEEE Internatl. Conv. Rec., Pt. 7, pp. 183-208 (1966).
[17] Vongpanitlerd, S., & B. D. O. Anderson, Scattering matrix synthesis via reactance extraction. IEEE Transactions on Circuit Theory CT-17, 511-517 (1970). · doi:10.1109/TCT.1970.1083180
[18] Anderson, B. D. O., The inverse problem of stationary covariance generation. Journal of Statistical Physics 1, 133-147 (1969). · doi:10.1007/BF01007246
[19] Willems, J. C., Stationary Covariance Generation via the Algebraic Riccati Equation. Fourth UKAC Control Convention, Manchester, England, 1971.
[20] Breuer, S., & E. T. Onat, On recoverable work in linear viscoelasticity. ZAMP 15, 12-21 (1964). · Zbl 0123.40802 · doi:10.1007/BF01602660
[21] Gantmacher, F. R., The Theory of Matrices. New York: Chelsea 1959. · Zbl 0085.01001
[22] McMillan, B., Introduction to formal realizability theory, I and II. Bell System Tech. J. 31, 217-279 and 541-600 (1952).
[23] Meixner, J., Thermodynamic Theory of Relaxation Phenomena, pp. 73-89 in: Non-Equilibrium Thermodynamics, Variational Techniques and Stability (R. J. Donnelly, R. Herman, & I. Prigogine, Eds.). The University of Chicago Press 1966.
[24] Truesdell, C., Rational Thermodynamics. New York: McGraw-Hill 1969.
[25] Newcomb, R. W., Linear Multiport Synthesis. New York: McGraw-Hill 1966.
[26] Widder, D. V., The Laplace Transform. Princeton University Press 1946. · Zbl 0060.24801
[27] Weiss, L., & R. E. Kalman, Contributions to linear system theory. Int. J. Engrg. Sci. 3, 141-171 (1965). · Zbl 0136.08702 · doi:10.1016/0020-7225(65)90042-X
[28] Belevitch, V., Classical Network Synthesis. Princeton: Van Nostrand 1968. · Zbl 0172.20404
[29] Gurtin, M. E., & E. Sternberg, On the linear theory of viscoelasticity. Arch. Rational Mech. Anal. 11, 291-356 (1962). · Zbl 0107.41007 · doi:10.1007/BF00253942
[30] Day, W. A., Time-reversal and the symmetry of the relaxation function of the linear viscoelastic material. Arch. Rational Mech. Anal. 40, 149-159 (1971). · Zbl 0216.51104 · doi:10.1007/BF00281479
[31] Brockett, R. W., & R. A. Skoog, A New Perturbation Theory for the Synthesis of Non-linear Networks, pp. 17-33 of the SIAM-AMS Proceedings on: Mathematical Aspects of Electrical Network Analysis. Am. Math. Soc., 1971. · Zbl 0247.94024
[32] Gurtin, M. E., & I. Herrera, On dissipation inequalities and linear viscoelasticity. Quart. Appl. Math. 23, 235-245 (1965). · Zbl 0173.52703
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