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Closed-loop structure of decouplable linear multivariable systems. (English) Zbl 1249.93079
Summary: Considering a controllable, square, linear multivariable system, which is decouplable by static state feedback, we completely characterize in this paper the structure of the decoupled closed-loop system. The family of all attainable transfer function matrices for the decoupled closed-loop system is characterized which also completely establishes all possible combinations of attainable finite pole and zero structures. The set of assignable poles as well as the set of fixed decoupling poles are determined, and decoupling is achieved avoiding unnecessary cancellations of invariant zeros. For a particular attainable decoupled closed-loop structure, it is shown how to find the corresponding state feedback, and it is proved that this feedback is unique if and only if the system is controllable.

93B52 Feedback control
93B11 System structure simplification
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
93B55 Pole and zero placement problems
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[1] Descusse J., Dion J. M.: On the structure at infinity of linear square decoupled systems. IEEE Trans. Automat. Control AC-27 (1982), 971-974 · Zbl 0485.93042 · doi:10.1109/TAC.1982.1103041
[2] Falb P. L., Wolovich W. A.: Decoupling in the design and synthesis of multivariable control systems. IEEE Trans. Automat. Control AC-12 (1967), 651-659 · doi:10.1109/TAC.1967.1098737
[3] Hautus M. L. J., Heymann M.: Linear feedback: An algebraic approach. SIAM J. Control Optim. 16 (1978), 83-105 · Zbl 0385.93015 · doi:10.1137/0316007
[4] Herrera A.: Static realization of dynamic precompensators. IEEE Trans. Automat. Control 37 (1992), 1391-1394 · Zbl 0755.93042 · doi:10.1109/9.159579
[5] Kailath T.: Linear Systems. Prentice Hall, Englewood Cliffs, NJ 1980 · Zbl 0870.93013 · doi:10.1080/00207179608921730
[6] Koussiouris T. G.: A frequency domain approach for the block decoupling problem II. Pole assignment while block decoupling a minimal system by state feedback and a constant non-singular input transformation and observability of the block decoupled system. Internat. J. Control 32 (1980), 443-464 · Zbl 0449.93005 · doi:10.1080/00207178008922867
[7] Kučera V., Zagalak P.: Fundamental theorem of state feedback for singular systems. Automatica 24 (1988), 653-658 · Zbl 0661.93033 · doi:10.1016/0005-1098(88)90112-4
[8] Kučera V., Zagalak P.: Constant solutions of polynomial equations. Internat. J. Control 53 (1991), 495-502 · Zbl 0731.15009 · doi:10.1080/00207179108953630
[9] MacFarlane A. G. J., Karcanias N.: Poles and zeros of linear multivariable systems: A survey of the algebraic, geometric and complex-variable theory. Internat. J. Control 24 (1976), 33-74 · Zbl 0374.93014 · doi:10.1080/00207177608932805
[10] Martínez-García J. C., Malabre M.: The row by row decoupling problem with stability: A structural approach. IEEE Trans. Automat. Control 39 (1994), 2457-2460 · Zbl 0825.93252 · doi:10.1109/9.362849
[11] Rosenbrock H. H.: State-Space and Multivariable Theory. Wiley, New York 1970 · Zbl 0246.93010
[12] Ruiz-León J., Zagalak, P., Eldem V.: On the Morgan problem with stability. Kybernetika 32 (1996), 425-441 · Zbl 0885.34055 · www.kybernetika.cz · eudml:27972
[13] Vardulakis A. I. G.: Linear Multivariable Control: Algebraic and Synthesis Methods. Wiley, New York 1991 · Zbl 0751.93002
[14] Wonham W. M., Morse A. S.: Decoupling and pole assignment in linear multivariable systems: A geometric approach. SIAM J. Control 8 (1970), 1-18 · Zbl 0206.16404 · doi:10.1137/0308001
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