Geodesic
A necessary and sufficient condition for static output feedback stabilizability of linear discrete-time systems
Kybernetika, Tome 39 (2003) no. 4, pp. 447-459
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Necessary and sufficient conditions for a discrete-time system to be stabilizable via static output feedback are established. The conditions include a Riccati equation. An iterative as well as non-iterative LMI based algorithm with guaranteed cost for the computation of output stabilizing feedback gains is proposed and introduces the novel LMI approach to compute the stabilizing output feedback gain matrix. The results provide the discrete- time counterpart to the results by Kučera and De Souza.
Necessary and sufficient conditions for a discrete-time system to be stabilizable via static output feedback are established. The conditions include a Riccati equation. An iterative as well as non-iterative LMI based algorithm with guaranteed cost for the computation of output stabilizing feedback gains is proposed and introduces the novel LMI approach to compute the stabilizing output feedback gain matrix. The results provide the discrete- time counterpart to the results by Kučera and De Souza.
Classification : 90C55, 93B52, 93C55, 93D15
Keywords: discrete-time systems; output feedback; stabilizability; stabilizing feedback; Riccati equations; LMI approach 
@article{KYB_2003_39_4_a3,
     author = {Rosinov\'a, Danica and Vesel\'y, Vojtech and Ku\v{c}era, Vladim{\'\i}r},
     title = {A necessary and sufficient condition for static output feedback stabilizability of linear discrete-time systems},
     journal = {Kybernetika},
     pages = {447--459},
     year = {2003},
     volume = {39},
     number = {4},
     mrnumber = {2024525},
     zbl = {1249.93150},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2003_39_4_a3/}
}
TY  - JOUR
AU  - Rosinová, Danica
AU  - Veselý, Vojtech
AU  - Kučera, Vladimír
TI  - A necessary and sufficient condition for static output feedback stabilizability of linear discrete-time systems
JO  - Kybernetika
PY  - 2003
SP  - 447
EP  - 459
VL  - 39
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_2003_39_4_a3/
LA  - en
ID  - KYB_2003_39_4_a3
ER  - 
%0 Journal Article
%A Rosinová, Danica
%A Veselý, Vojtech
%A Kučera, Vladimír
%T A necessary and sufficient condition for static output feedback stabilizability of linear discrete-time systems
%J Kybernetika
%D 2003
%P 447-459
%V 39
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_2003_39_4_a3/
%G en
%F KYB_2003_39_4_a3
Rosinová, Danica; Veselý, Vojtech; Kučera, Vladimír. A necessary and sufficient condition for static output feedback stabilizability of linear discrete-time systems. Kybernetika, Tome 39 (2003) no. 4, pp. 447-459. http://geodesic.mathdoc.fr/item/KYB_2003_39_4_a3/

[1] Boyd S., Ghaoui L. El, Feron, E., Balakrishnan V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia 15 (1994) | MR | Zbl

[2] Crusius C. A. R., Trofino A.: Sufficient LMI Conditions for output feedback control problems. IEEE Trans. Automat. Control 44 (1999), 1053–1057 | DOI | MR | Zbl

[3] Souza C. E. De, Trofino A.: An LMI Approach to stabilization of linear discrete-time periodic systems. Internat. J. Control 73 (2000), 696–703 | DOI | MR | Zbl

[4] Ghaoui L. El, Balakrishnan V.: Synthesis of fixed structure controllers via numerical optimization. In: Proc. 33rd Conference on Decision and Control, Lake Buena Vista (FL) 1994, pp. 2678–2683

[5] Goh K. C., Safonov M. G., Papavassilopoulos G. P.: Global optimization for the biaffine matrix inequality problem. J. Global Optimization 7 (1995), 365–380 | DOI | MR | Zbl

[6] Keel L. H., Bhattacharyya S. P., Howze J. W.: Robust control with structured perturbations. IEEE Trans. Automat. Control 33 (1988), 68–78 | DOI | MR | Zbl

[7] Kolla S. R., Farison J. B.: Reduced-order dynamic compensator design for stability robustness of linear discrete-time systems. IEEE Trans. Automat. Control 36 (1991), 1077–1081 | DOI | MR | Zbl

[8] Kučera V., Souza C. E. De: A necessary and sufficient condition for output feedback stabilizability. Automatica 31 (1995), 1357–1359 | DOI | MR

[9] Levine W. S., Athans M.: On the determination of the optimal constant output feedback gains for linear multivariable systems. IEEE Trans. Automat. Control 15 (1970), 44–49 | DOI | MR

[10] Sharav-Schapiro N., Palmor Z. J., Steinberg A.: Output stabilizing robust control for discrete uncertain systems. Automatica 34 (1998), 731–739 | DOI | MR | Zbl

[11] Trinh H., Aldeen M.: Design of suboptimal decentralized output feedback controllers for interconnected power system. In: Proc. IMACS Symposium Modeling and Control of Technological System, Casablanca 1991, Vol. 1, pp. 313–319

[12] Veselý V.: Static output feedback controller design. Kybernetika 37 (2001), 205–221 | MR

[13] Zhou K. K., Doyle J. C., Glover K.: Robust and Optimal Control. Prentice Hall, Englewood Cliffs, N.J. 1996 | Zbl