Previous |  Up |  Next


expanding system; stabilizing controller; disturbance rejection; tracking; stable rational functions
The problem of designing realistic decentralized controller to solve a servomechanism problem in the framework of “large scale systems” is considered in this paper. As any large scale system is built by expanding construction of one subsystem being connected to the existing system. In particular, it is desired to find a local stabilizing controller in terms of a free parameter (belonging to the ring of proper stable transfer functions) so that desirable properties of the controlled system, such as tracking and/or disturbance rejection for any arbitrary deterministic signal along with stabilization of the expanded overall system occur. An algorithm for designing such a free controller parameter is presented. The necessary and sufficient conditions for the existence of solutions to the Expanding Systems with Tracking and/or Disturbance Rejection Problem are established here and characterized the corresponding full set of stabilizing controllers that solve the problem. A numerical example is presented to illustrate the design procedure of the proposed controller for the Expanded System.
[1] Baksi D., Patel V. V., Datta K. B., Ray G. D.: Decentralized stabilization and strong stabilzation of a bicoprime factorized plant. Kybernetika 35 (1999), 235–253 MR 1690949
[2] Davision E. J., Gesing W.: Sequential stability and optimization of large scale decentralized systems. Automatica 15 (1979), 307–324 DOI 10.1016/0005-1098(79)90047-5 | MR 0543844
[3] Davison E. J., Ozgüner U.: The expanding system problem. Systems and Control Letters 1 (1982), 255–260 DOI 10.1016/S0167-6911(82)80008-X | MR 0670208
[4] Francis B. A.: A Course in $H_{\infty }$ Control Theory. Springer Verlag, Berlin 1987
[5] Ikeda M.: Decentralized control of large scale systems. In: Three Decades of Mathematical System Theory: A Collection of Surveys on the Occasion of the Fiftieth Birthday of Jan C. Willems (Lecture Notes in Control and Information Sciences 135, H. Nijmeijer and J. M. Schumacher, eds.). Springer Verlag, Berlin 1989, pp. 219–242 MR 1025792 | Zbl 0683.93009
[6] Ikeda M., Siljak D. D.: On decentrally stabilizable large-scale systems. Automatica 16 (1980), 331–334 DOI 10.1016/0005-1098(80)90042-4 | MR 0575188 | Zbl 0432.93004
[7] Patel V. V., Datta K. B.: A dual look at unity interpolation in $H_{\infty }$. Internat. J. Control 62 (1995), 813–829 DOI 10.1080/00207179508921570 | MR 1632914
[8] Saeks R., Murray J.: Feedback system design: The tracking and disturbance rejection problems. IEEE Trans. Automatic Control 26 (1981), 203–217 DOI 10.1109/TAC.1981.1102561
[9] Saeks R., Murray J. J.: Fractional representations, algebraic geometry and the simultaneous stabilization problem. IEEE Trans. Automatic Control 27 (1982), 895–903 DOI 10.1109/TAC.1982.1103005 | MR 0680490
[10] Tan X. L., Ikeda M.: Decentralized stabilization for expanding construction of large scale systems. IEEE Trans. Automatic Control 35 (1990), 664–651 MR 1055494 | Zbl 0800.93065
[11] Tan X. L., Ikeda M.: Expanding construction of large scale servosystems. In: Proc. 2nd Japan–China Joint Symposium on System and Control Theory and Applications 1990
[12] Tan X. L., Ikeda M.: Expanding construction of large scale servosystems. In: IMACS World Congress, Dublin, Ireland 1991
[13] Vidyasagar M.: Control System Synthesis: A Factorization Approach. MIT Press, Cambridge, MA 1985 MR 0787045 | Zbl 0655.93001
[14] Youla D. C., Bongiorno J. J., Lu C. N.: Single loop feedback stabilization of linear multivariable dynamical plants. Automatica 10 (1974), 155–173 DOI 10.1016/0005-1098(74)90021-1 | MR 0490293 | Zbl 0276.93036
Partner of
EuDML logo