Login | Register

Simultaneous LQ control of a set of LTI systems using constrained generalized sampled-data hold functions


Simultaneous LQ control of a set of LTI systems using constrained generalized sampled-data hold functions

Lavaei, Javad and Aghdam, Amir G. (2007) Simultaneous LQ control of a set of LTI systems using constrained generalized sampled-data hold functions. Automatica, 43 (2). pp. 274-280. ISSN 00051098

[thumbnail of Aghdam2006b.pdf]
Text (application/pdf)
Aghdam2006b.pdf - Accepted Version

Official URL: http://dx.doi.org/10.1016/j.automatica.2006.08.013


In this paper, sampled-data control of a set of continuous-time LTI systems is considered. It is assumed that a predefined guaranteed continuous-time quadratic cost function, which is, in fact, the sum of the performance indices for all systems, is given. The main objective here is to design a decentralized periodic output feedback controller with a prespecified form, e.g., polynomial, piecewise constant, exponential, etc., which minimizes the above mentioned guaranteed cost function. This problem is first formulated as a set of matrix inequalities, and then by using a well-known technique, it is reformulated as a LMI problem. The set of linear matrix inequalities obtained provides necessary and sufficient conditions for the existence of a decentralized optimal simultaneous stabilizing controller with the prespecified form (rather than a general form). Moreover, an algorithm is presented to solve the resultant LMI problem. Finally, the efficiency of the proposed method is demonstrated in two numerical examples.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Electrical and Computer Engineering
Item Type:Article
Authors:Lavaei, Javad and Aghdam, Amir G.
Journal or Publication:Automatica
Digital Object Identifier (DOI):10.1016/j.automatica.2006.08.013
Keywords:Simultaneous stabilization; H2 optimal control; Generalized sampled-data hold function; Decentralized; LMI
ID Code:975164
Deposited By: Danielle Dennie
Deposited On:22 Jan 2013 13:45
Last Modified:18 Jan 2018 17:39


Blondel and Gevers, 1993 V. Blondel, M. Gevers Simultaneous stabilizability of three linear systems is rationally undecidable Mathematics of Control, Signals, and Systems, 6 (2) (1993), pp. 135–145

Cao and Lam, 2001 Y.Y. Cao, J. Lam A computational method for simultaneous LQ optimal control design via piecewise constant output feedback IEEE Transactions on Systems, Man, and Cybernetics, 31 (5) (2001), pp. 836–842

Cao et al., 1999 Y.Y. Cao, Y.X. Sun, J. Lam Simultaneous stabilization via static output feedback and state feedback IEEE Transactions on Automatic Control., 44 (6) (1999), pp. 1277–1282

Chammas and Leondes, 1978 A.B. Chammas, C.T. Leondes On the design of linear time-invariant systems by periodic output feedback: Part I, discrete-time pole placement International Journal of Control, 27 (1978), pp. 885–894

Davison and Chang, 1990 E.J. Davison, T.N. Chang Decentralized stabilization and pole assignment for general proper systems IEEE Transactions on Automatic Control, 35 (6) (1990), pp. 652–664

Feuer and Goodwin, 1994 A. Feuer, G.C. Goodwin Generalized sample hold functions-frequency domain analysis of robustness, sensitivity, and intersample difficulties IEEE Transactions on Automatic Control, 39 (5) (1994), pp. 1042–1047

Fonte et al., 2001 C. Fonte, M. Zasadzinski, C. Bernier-Kazantsev, M. Darouach On the simultaneous stabilization of three or more plants IEEE Transactions on Automatic Control, 46 (7) (2001), pp. 1101–1107

Howitt and Luus, 1993 G.D. Howitt, R. Luus Control of a collection of linear systems by linear state feedback control International Journal of Control, 58 (1993), pp. 79–96

Hyslop et al., 1992 G.L. Hyslop, H. Schattler, T.J. Tarn Descent algorithms for optimal periodic output feedback control IEEE Transactions on Automatic Control, 37 (12) (1992), pp. 1893–1904

Jia and Ackermann, 2001 Y. Jia, J. Ackermann Condition and algorithm for simultaneous stabilization of linear plants Automatica, 37 (9) (2001), pp. 1425–1434

Kabamba, 1987 P.T. Kabamba Control of linear systems using generalized sampled-data hold functions IEEE Transactions on Automatic Control, 32 (9) (1987), pp. 772–783

Kabamba and Yang, 1991 P.T. Kabamba, C. Yang Simultaneous controller design for linear time-invariant systems IEEE Transactions on Automatic Control, 36 (1) (1991), pp. 106–111

Lavaei and Aghdam, 2006 Lavaei, J., & Aghdam, A. G. (2006). High-performance simultaneous stabilizing periodic feedback control with a constrained structure. Proceedings of the 2006 American control conference (pp. 839–844). Minneapolis, USA.

Miller and Rossi, 2001 D.E. Miller, M. Rossi Dimultaneous stabilization with near optimal LQR performance IEEE Transactions on Automatic Control, 46 (10) (2001), pp. 1543–1555

Tarn and Yang, 1988 Tarn, T. J., & Yang, T., 1988. Simultaneous stabilization of infinite-dimensional systems with periodic output feedback. Linear circuit systems and signals processing: Theory and application (pp. 409–424).

Toker and Özbay, 1995 Toker, O., & Özbay, H. (1995). On the NP-hardness of solving bilinear matrix inequalities and simultaneous stabilization with static output feedback. Proceedings of the 1995 American control conference (pp. 2525–2526). Seattle, Washington.

Vidyasagar and Viswanadham, 1982 M. Vidyasagar, N. Viswanadham Algebraic design techniques for reliable stabilization IEEE Transactions on Automatic Control, 27 (5) (1982), pp. 1085–1095

Wang, 1982 S.H. Wang Stabilization of decentralized control systems via time-varying controllers IEEE Transactions on Automatic Control, 27 (3) (1982), pp. 741–744

Werner, 1996 Werner, H., 1996. An iterative algorithm for suboptimal periodic output feedback control. UKACC international conference on control (pp. 814–818).

Youla et al., 1974 D. Youla, J. Bongiorno, C. Lu Single-loop feedback stabilization of linear multivariable dynamical plants Automatica, 10 (2) (1974), pp. 159–173
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Downloads per month over past year

Research related to the current document (at the CORE website)
- Research related to the current document (at the CORE website)
Back to top Back to top