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Generalized model matching and (F,G)-invariant submodules for linear systems over rings. (English) Zbl 0523.93029

MSC:
93B25 Algebraic methods
13A99 General commutative ring theory
93D15 Stabilization of systems by feedback
13C99 Theory of modules and ideals in commutative rings
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
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[1] Wolovich, W.A., Linear multivariable systems, (1974), Springer New York · Zbl 0291.93002
[2] Forney, G.D., Minimal bases of rational vector spaces with applications to multivariable linear systems, SIAM J. control, 13, 493-520, (1975) · Zbl 0269.93011
[3] Emre, E., The polynomial equation QQc+rpc=φ with application to dynamic feedback, SIAM J. control optim., 18, 611-620, (1980) · Zbl 0505.93016
[4] Emre, E.; Hautus, M.L.J., A polynomial characterization of (A,B)-invariant and reachability subspaces, SIAM J. control optim., 18, 420-436, (1980) · Zbl 0452.93011
[5] Emre, E.; Khargonekar, P.P., Regulation of split linear systems over rings: coefficient-assignment and observers, IEEE trans. automat. control, (1982) · Zbl 0502.93019
[6] Emre, E., Pole assignment by dynamic feedback, Internat. J. control, 33, 2, 311-321, (1981) · Zbl 0455.93025
[7] Bourbaki, N., Commutative algebra, (1972), Addison-Wesley
[8] Khargonekar, P.P., On matrix fraction representations for linear systems over commutative rings, SIAM J. control optim., (1982) · Zbl 0517.93015
[9] Wonham, W.M.; Morse, A.S., Feedback invariants of linear multivariable systems, Automatica, 8, 93-100, (1972) · Zbl 0235.93007
[10] Emre, E.; Silverman, L.M.; Glover, K., Generalized dynamic covers for linear systems with applications to deterministic identification and realization problems, IEEE trans. automat. control, AC-22, 25-36, (1977)
[11] Morse, A.S., Minimal solutions to transfer matrix equations, IEEE trans. automat. control, AC-21, 131-133, (1976) · Zbl 0321.93012
[12] Emre, E.; Silverman, L.M., Minimal dynamic inverses for linear systems with arbitrary initial states, IEEE trans. automat. control, AC-21, 766-769, (1976) · Zbl 0334.93018
[13] Emre, E.; Silverman, L.M., K-observers for linear systems with unknown inputs, IEEE trans. automat. control, AC-25, 779-782, (1980) · Zbl 0462.93012
[14] Emre, E.; Silverman, L.M., Partial model matching of linear systems, IEEE trans. automat. control, AC-21, 131-133, (1980) · Zbl 0432.93026
[15] Wonham, W.M., Dynamic observers: geometric theory, IEEE trans. automat. control, AC-15, 258-259, (1970)
[16] Wonham, W.M., Linear multivariable control: A geometric approach, (1974), Springer Berlin · Zbl 0314.93008
[17] Rosenbrock, H.H., State space and multivariable theory, (1970), Wiley New York · Zbl 0246.93010
[18] Fuhrmann, P.A.; Willems, J.C., A study of (A,B)-invariant subspaces via polynomial models, Internat. J. control, 467-494, (1980) · Zbl 0489.93014
[19] Hautus, M.L.J., A frequency domain treatment of disturbance decoupling and output stabilization, () · Zbl 0455.93015
[20] Khargonekar, P.P.; Emre, E., Further results on polynomial characterizations of (F,G)-invariant subspaces, IEEE trans. automat. control, (1982) · Zbl 0502.93019
[21] Emre, E., Nonsingular factors of polynomial matrices and (A,B)-invariant subspaces, SIAM J. control optim., 18, (1980) · Zbl 0439.93031
[22] Wolovich, W.A.; Antsaklis, P.; Elliott, H., On the stability of solutions to minimal and nonminimal design problems, IEEE trans. automat. control, AC-22, 88-93, (1972) · Zbl 0346.93037
[23] Moore, B.C.; Silverman, L.M., Model matching by state feedback and dynamic compensation, IEEE trans. automat. control, AC-17, 491-497, (1972) · Zbl 0263.93033
[24] Wang, S.H.; Davison, E.J., A minimization algorithm for the design of linear multivariable systems, IEEE trans. automat. control, AC-18, 220-225, (1973) · Zbl 0261.93010
[25] M.K. Sain, A free modular algorithm for minimal design of linear multivariable systems, in 1975 IFAC Congress, Paper 9.1.
[26] Morse, A.S., Structure and design of linear model following systems, IEEE trans. automat. control, AC-18, 346-354, (1973) · Zbl 0264.93005
[27] Emre, E., A new approach to identification of linear systems and the optimal solution of a class of synthesis problems, Ieee cdc, (1981), San Diego
[28] Eising, R.; Emre, E., Exact model matching of 2-D systems, IEEE trans. automat. control, 132-133, (1979)
[29] Fuhrmann, P.A., On strict system equivalence and similarity, Internat. J. control, 25, 5-10, (1977) · Zbl 0357.93009
[30] Emre, E., On a natural realization of matrix fraction descriptions, IEEE trans. automat. control, AC-25, 288-289, (1980) · Zbl 0438.93021
[31] E.W. Kamen, Lectures on algebraic system theory: linear systems over rings
[32] Sontag, E.D., Linear systems over commutative rings, a (partial) update survey, IFAC conference, (1981), Japan · Zbl 0522.93020
[33] Emre, E., On necessary and sufficient conditions for regulation of linear systems over rings, SIAM J. control optim., (1982) · Zbl 0521.93015
[34] Desoer, C.A.; Liu, R.W.; Murray, J.; Saeks, R., Feedback system design: the fractional representation approach to analysis and synthesis, IEEE trans. automat. control, AC-25, 399-412, (1980) · Zbl 0442.93024
[35] Morse, A.S., Global stability of parameter-adaptive control systems, IEEE trans. automat. control, AC-25, 433-439, (1980) · Zbl 0438.93042
[36] Kalman, R.E.; Falb, P.L.; Arbib, M.A., Topics in mathematical system theory, (1969), McGraw-Hill New York · Zbl 0231.49001
[37] Newman, M., Integral matrices, (1972), Academic · Zbl 0254.15009
[38] Khargonekar, P.P.; Emre, E., Further results on polynomial characterizations of (F,G)-invariant subspaces, (1980), Center for Mathematical System Theory, Univ. of Florida Gainesville, Fla
[39] Wyman, B.F.; Sain, M.K., The zero module and essential inverse systems, IEEE trans. circuits and systems, CAS-28, 112-126, (1981) · Zbl 0474.93023
[40] Silverman, L.M., Inversion of multivariable linear systems, IEEE trans. automat. control, 14, (1969) · Zbl 0206.14601
[41] Sain, M.K.; Massey, J.L., Invertibility of linear time-invariant dynamical systems, IEEE trans. automat. control, 14, 141-149, (1969)
[42] B.C. Moore and L.M. Silverman, A time domain characterization of the invariant factors of system transfer function, in Proceedings of the 1974 JACC.
[43] Hautus, M.L.J., Controlled invariance in systems over rings, () · Zbl 0493.93010
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