Previous |  Up |  Next


linear systems; multivariable systems; feedback control; pole and zero placement problems
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.
[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 DOI 10.1109/TAC.1982.1103041 | MR 0680500 | Zbl 0485.93042
[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 DOI 10.1137/0316007 | MR 0476024 | Zbl 0385.93015
[4] Herrera A.: Static realization of dynamic precompensators. IEEE Trans. Automat. Control 37 (1992), 1391–1394 DOI 10.1109/9.159579 | MR 1183101 | Zbl 0755.93042
[5] Kailath T.: Linear Systems. Prentice Hall, Englewood Cliffs, NJ 1980 MR 0569473 | Zbl 0870.93013
[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 DOI 10.1080/00207178008922867 | MR 0587180
[7] Kučera V., Zagalak P.: Fundamental theorem of state feedback for singular systems. Automatica 24 (1988), 653–658 DOI 10.1016/0005-1098(88)90112-4 | MR 0966689
[8] Kučera V., Zagalak P.: Constant solutions of polynomial equations. Internat. J. Control 53 (1991), 495–502 DOI 10.1080/00207179108953630 | MR 1091157
[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 DOI 10.1080/00207177608932805 | MR 0418989 | Zbl 0374.93014
[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 DOI 10.1109/9.362849 | MR 1337570 | Zbl 0825.93252
[11] Rosenbrock H. H.: State-Space and Multivariable Theory. Wiley, New York 1970 MR 0325201 | Zbl 0246.93010
[12] Ruiz-León J., Zagalak, P., Eldem V.: On the Morgan problem with stability. Kybernetika 32 (1996), 425–441 MR 1420133
[13] Vardulakis A. I. G.: Linear Multivariable Control: Algebraic and Synthesis Methods. Wiley, New York 1991 MR 1104222
[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 DOI 10.1137/0308001 | MR 0270771 | Zbl 0206.16404
[15] Zúñiga J.C., Ruiz-León, J., Henrion D.: Algorithm for decoupling and complete pole assignment of linear multivariable systems. In: Proc. European Control Conference ECC-2003, Cambridge 2003
Partner of
EuDML logo