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On the Morgan problem with stability. (English) Zbl 0885.34055
The authors consider a linear, controllable, right invertible system of the form \[ \begin{cases} \dot x= Ax+Bu\\ y =Cx\end{cases} \] They are interested in the Morgan (decoupling) problem with stability. It consists in finding feedback laws \(u= Fx+Gv\) which put the transfer function into a diagonal form, while ensuring at the same time internal stability. For the solution of this problem, the authors give necessary and sufficient conditions. The method relies on the basic properties of the ring of proper and stable rational functions over \(\mathbb{R}\).

MSC:
34H05 Control problems involving ordinary differential equations
93B27 Geometric methods
93B11 System structure simplification
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References:
[1] U. Başer, V. Eldem: Diagonal decoupling problem with internal stability: A solution by dynamic output feedback and constant precompensator. 3rd IFAC Conference on System Structure and Control, Nantes, France, 5-7 July 1995.
[2] J. Descusse J. F. Lafay, M. Malabre: Solution to Morgan’s problem. IEEE Trans. Automat. Control 33 (1988), 8, 732-739. · Zbl 0656.93018 · doi:10.1109/9.1289
[3] J. M. Dion, C. Commault: The minimal delay decoupling problem: Feedback implementation with stability. SIAM J. Control Optim. 26 (1988), 1, 66-82. · Zbl 0646.93049 · doi:10.1137/0326005
[4] V. Eldem: Feedback realization of open loop diagonalizers. Kybernetika 29 (1993), 5, 406-416. · Zbl 0811.93027 · www.kybernetika.cz · eudml:27699
[5] V. Eldem: The solution of diagonal decoupling problem by dynamic output feedback and constant precompensator: The general case. IEEE Trans. Automat. Control 39 (1994), 3, 503-511. · Zbl 0812.93035 · doi:10.1109/9.280749
[6] P. L. Falb, W. A. Wolovich: Decoupling in the design and synthesis of multivariable control systems. IEEE Trans. Automat. Control AC-12 (1967), 6, 651-659.
[7] A. Herrera: On the static realization of dynamic precompensators and some related problems. Proceedings 1st European Control Conference, Grenoble, France 1991.
[8] A. Herrera J. F. Lafay, P. Zagalak: A semicanonical form for a class of right invertible systems. Preprints IFAC Conference on System Structure and Control, Nantes, France 1995, pp. 590-594.
[9] V. Kučera, A. Herrera: Static realization of dynamic precompensators for descriptor systems. Systems Control Lett. 16 (1991), 273-276. · Zbl 0728.93037 · doi:10.1016/0167-6911(91)90015-7
[10] V. Kučera, P. Zagalak: Constant solutions of polynomial equations. Internat. J. Control 53 (1991), 2, 495-502. · Zbl 0731.15009
[11] M. Malabre V. Kučera, P. Zagalak: Reachability and controllability indices for linear descriptor systems. Systems Control Lett. 15 (1990), 119-123. · Zbl 0715.93008 · doi:10.1016/0167-6911(90)90005-F
[12] J. C. Martinez Garcia, M. Malabre: The row by row decoupling problem with stability. IEEE Trans. Automat. Control · Zbl 0825.93252 · doi:10.1109/9.362849
[13] B. S. Morgan, Jr.: The synthesis of linear multivariable systems by state-variable feedback. IEEE Trans. Automat. Control AC-9 (1964), 405-411.
[14] A. S. Morse, W. M. Wonham: Status of noninteracting control. IEEE Trans. Automat. Control AC-16 (1971), 6, 568-581.
[15] L. Pernebo: An algebraic theory for the design of controllers for linear multivariable systems. Parts I and II. IEEE Trans. Automat. Control AC-26 (1981), 1, 171-182 and 183-194. · Zbl 0467.93040 · doi:10.1109/TAC.1981.1102554
[16] J. Ruiz: Decoupling of Linear Systems. Ph.D. Thesis. Czech Technical University, Prague 1996.
[17] P. Zagalak J. F. Lafay, A. Herrera: The row-by-row decoupling via state feedback: A polynomial approach. Automatica 29 (1993), 6, 1491-1499. · Zbl 0790.93075 · doi:10.1016/0005-1098(93)90012-I
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