Abstract
This paper refers to the problem of designing a linear state feedback dynamic controller for single-input, single-output decoupling of linear, time-invariant, singular systems. Sufficient conditions are established for the state-feedback decoupling problem to have a solution. In the case where the system satisfies these conditions, the class of controller matrices which decouple the system is given. Finally a method is presented for pole-zero placement in the decoupled singular system and a structure is described for the realization of the generalized transfer function matrices.
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References
P.L. Falb and W.A. Wolovich, “Decoupling in the design and synthesis of multivariable control systems,”IEEE Trans. Autom. Contr., Vol.AC-12, pp. 651–659, 1967.
E.G. Gilbert, “The decoupling of multivariable systems by state feedback,”SIAM. J. Control., Vol.7, pp. 50–63, 1969.
W.M. Wonham and A.S. Morse, “Decoupling and pole assignment in linear systems: A geometric approach,”SIAM J. Contr., Vol.8, pp. 1–18, 1970.
A.S. Morse and W.M. Wonham, “Decoupling and pole assignment by dynamic compensation,”SIAM J. Control., Vol.8, pp. 317–337, 1970.
A.S. Morse and W.M. Wonham, “Status of non-interactive control,”IEEE Trans. on Autom. Contr., Vol.AC-16, pp. 568–581, 1971.
L.M. Silverman, “Decoupling with state feedback and precompensation,”IEEE Trans. on Autom. Contr., Vol.AC-15, pp. 487–489, 1970.
J.W. Howze and J.B. Pearson, “Decoupling and arbitrary pole placement in linear systems using output feedback,”IEEE Trans. on Autom. Contr., Vol.AC-15, pp. 660–663, 1970.
I.H. Mufti, “A note on the decoupling of multivariable systems,”IEEE Trans. Autom. Contr., Vol.AC-14, p. 415, 1969.
J.W. Howze, “Necessary and sufficient conditions for decoupling using output feedback,”IEEE Trans. Autom. Contr., Vol.AC-18, pp. 44–46, 1973.
W.A. Porter, “Decoupling and inverses for time varying linear systems,”IEEE Trans. Autom. Contr., Vol.AC-14, pp. 378–380, 1969.
A.K. Majumdar and A.K. Choudhury, “On the decoupling of nonlinear systems,”Int. J. Control, Vol.16, pp. 705–718, 1972.
B.G. Mertzios, “Sensitivity-Factorization-Decoupling of linear multivariable 2-D systems,” Ph.D. Thesis, Department of Electrical Engineering, Democritus U. of Thrace, Xanthi, Greece, 1982.
G.C. Verghese, P. Van Dooren and T. Kailath, “Properties of the system matrix of a generalized state space system,”Int. J. Control, Vol.30, pp. 235–243, 1979.
G.C. Verghese, B.C. Lévy and T. Kailath, “A generalized state space for singular systems,”IEEE Trans. on Autom. Contr., Vol.AC-26, pp. 811–830, 1981.
R.F. Sincovec, A.M. Erisman, E.L. Yip and M.A. Epton, “Analysis of descriptor systems using numerical algorithms,”IEEE Trans. onAutom. Contr., Vol.AC-26, pp. 139–147, 1981.
D. Cobb, “Feedback and pole placement in descriptor variable systems,”Int. J. Control, Vol.33, pp. 1135–1146, 1981.
E.L. Yip and R.F. Sincovec, “Solvability controllability and observability of continuous descriptor systems,”IEEE Trans. on Autom. Contr., Vol.AC-26, pp. 702–707, 1981.
A. J. J. Van Der Weiden and O.H. Bosgra, “The determination of structural properties of a linear multivariable system by operations of system similarity, 2. Non-proper systems in generalized state-space form,”Int. J. Control, Vol.32, pp. 489–537, 1980.
C.E. Langenhop, “Controllability and stabilizability of singular linear systems with constant coefficients,” Department of Mathematics, Southern Illinois University.
D.G. Luenberger, “Time invariant descriptor systems,”Automatica, Vol.14, pp. 473–480, 1978.
J.S. Thorp, “The singular pensil of a linear dynamical system,”Int. J. Control, Vol.18, pp. 577–596, 1973.
R.W. Newcomb, “The semistate description of nonlinear time variable circuits,”IEEE Trans. on Circ. and Syst., Vol.CAS-28, pp. 62–71, 1981.
P.V. Kokotovic, R.E. O'Malley Jr. and P. Sannuti, “Singular pertubations and order reduction in control theory—An overview,”Automatica, Vol.12, pp. 123–132, 1976.
M.M. Milic, “General passive networks — Solvability, degeneracies, and order of complexity,”IEEE Trans. on Circ. and Syst., Vol.CAS-21, pp. 177–183, 1974.
R.E. O'Malley Jr. and A. Jameson, “Singular pertubations and singular arcs, I,”IEEE Trans. on Autom. Control, Vol.AC-20, pp. 218–226, 1975.
M.A. Christodoulou, “Analysis and synthesis of singular systems,” Ph.D. Thesis, Department of Electrical Engineering, Democritus University of Thrace, Xanthi, Greece, 1984.
A.I.G. Vardulakis, D.N.J. Limebeer and N. Karkanias, “Structure and Smith-MacMillan form of a rational matrix at infinity,”Int. J. Control, Vol.35, pp. 701–725, 1982.
M.A. Christodoulou and B.G. Mertzios, “Realization of singular systems via Markov parameters,”Int. J. Control, Vol.42, pp. 1433–1441, 1985.
T. Kailath,Linear Systems, Prentice Hall, Englewood Cliffs, N.J., 1980.
S.H. Wang, “Design of linear multivariable systems,”Memo. No. ERL-M309, Electronics Research Lab, University of California, Berkely, 1971.
W.A. Wolovich, “The determination of state space representations for linear multivariable systems,”Proc. Second IFAC Symp. Multivariable Tech. Contr. Systems, Dusseldorf, 1971.
W.A. Wolovich and P.L. Falb, “On the structure of multivariable systems,”SIAM J. Control, Vol.7 pp. 437–451, 1969.
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Mertzios, B.G., Christodoulou, M.A. Decoupling and pole-zero assignment of singular systems with dynamic state feedback. Circuits Systems and Signal Process 5, 49–68 (1986). https://doi.org/10.1007/BF01600186
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DOI: https://doi.org/10.1007/BF01600186