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Keywords:
discrete-time systems; output feedback; stabilizability; stabilizing feedback; Riccati equations; LMI approach
discrete-time systems; output feedback; stabilizability; stabilizing feedback; Riccati equations; LMI approach
Summary:
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.
References:
[1] Boyd S., Ghaoui L. El, Feron, E., Balakrishnan V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia 15 (1994) MR 1284712 | Zbl 0816.93004
[2] Crusius C. A. R., Trofino A.: Sufficient LMI Conditions for output feedback control problems. IEEE Trans. Automat. Control 44 (1999), 1053–1057 DOI 10.1109/9.763227 | MR 1690555 | Zbl 0956.93028
[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 10.1080/002071700403466 | MR 1765380 | Zbl 1006.93578
[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 10.1007/BF01099648 | MR 1365801 | Zbl 0844.90083
[6] Keel L. H., Bhattacharyya S. P., Howze J. W.: Robust control with structured perturbations. IEEE Trans. Automat. Control 33 (1988), 68–78 DOI 10.1109/9.362 | MR 0920931 | Zbl 0652.93046
[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 10.1109/9.83542 | MR 1122487 | Zbl 0754.93064
[8] Kučera V., Souza C. E. De: A necessary and sufficient condition for output feedback stabilizability. Automatica 31 (1995), 1357–1359 DOI 10.1016/0005-1098(95)00048-2 | MR 1349414
[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 10.1109/TAC.1970.1099363 | MR 0274138
[10] Sharav-Schapiro N., Palmor Z. J., Steinberg A.: Output stabilizing robust control for discrete uncertain systems. Automatica 34 (1998), 731–739 DOI 10.1016/S0005-1098(97)00232-X | MR 1632118 | Zbl 0934.93060
[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 1839228
[13] Zhou K. K., Doyle J. C., Glover K.: Robust and Optimal Control. Prentice Hall, Englewood Cliffs, N.J. 1996 Zbl 0999.49500
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