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The third example has been borrowed from [11]. Let the nominal model matrices A,B,C be defined

,

,

.

The results of calculations are summarized in Table 3. , , , , , , .

Table 3. The results of calculation for example 3.

Gain matrix
-0.0808	-0.0966	-7.38	-7.4615	-7.1836
-0.2068	0.4640

Impact of S on closed loop system dynamic behavior the reader can consult in [11].

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5 Conclusion

In this paper, we have proposed new procedures for the LMI non-iterative static output feedback controller design. The feasible solutions of the output feedback controller design provide sufficient conditions guaranteeing quadratic stability with a guaranteed cost. The examples show the effectiveness of the proposed method.

Acknowledgement

The work has been supported by Grant No 1/3841/06 of the Slovak Scientific Grant Agency.

References

[1] BENTON, R. E.—SMITH, D. : Static Output Feedback Stabilization with Prescribed Degree of Stability, IEEE Trans. on AC 43 No. 10 (1993), 1493–1496.

[2] CHILALI, M.—GAHINET, P.—APKARIAN, P. : Robust Pole Placement in LMI Region., IEEE Trans on AC 44 No. 12 (1999), 2257–2267.

[3] De SOUZA—TROFINO, A. : An LMI Approach to Stabilization of Linear Discrete-Time Periodic Systems, Int. J. Control 73 (2000), 696–703.

[4] HAN, J.—SKELTON, R. E. : An LMI Optimization Approach For Structured Linear Controllers, In: Proc. 42th IEEE Conference on Decision and Control, Maui, 2003, pp. 5143–5148.

[5] IWASAKI, T.—SKELTON, R. E. : Linear Quadratic Suboptimal Control With Static Output Feedback, Systems and Control Letters 23 (1994), 421–430.

[6] KUˇCERA, V.—de SOUZA, C. : A Necessary and Sufficient Condition For Static Output Feedback Stabilizibility, Automatica 31 (1995), 1357–1359.

[7] LEVINE, W. S.—ATHANS, M. : On the Determination of the Optimal Constant Output Feedback Gains for Linear Multivariable Systems, IEEE Trans on AC 15 (1970), 44–49.

[8] M¨AKIL¨A, P. M. : Linear Quadratic Control Revisited, Automatica 36 (2000), 83–89.

[9] MOLINARRI, B. : The State Regulator Problem And Its Inverse, IEEE Trans. on AC AC-18 No. 5 (1973), 454–459.

[10] ROSINOV´A, D.—VESEL´Y, V.—KUˇCERA, V. : A Necessary and Sufficient Condition for Static Output Feedback Stabilizability of Linear Discrete-Time Systems, Kybernetika 39 No. 4 (2003), 447–459.

[11] ROSINOV´A, D.—VESEL´Y, V. : Robust PID Decentralized Controller Design Using LMI, Int. Journal of Computers, Communication and Control, Accepted, 2007.

[12] SKELTON, R. E.—IWASAKI, T.—GRIGORIADIS, K. : A Unified Algebraic Approach to Linear Control Design, Taylor and Francis, 1998.

[13] SYRMOS, V. L.—ABDALLAH, C. T.—DORATO, P.—GRIGORIADIS, K. : Static Output Feedback – A Survey, Automatica 33 No. 2 (1997), 125–137.

[14] VESEL´Y, V. : Static Output Feedback Controller Design, Kybernetika 37 No. 2 (2001), 205–221.

Received 4 October 2007

Vojtech Vesel´y(Prof, Ing, DrSc) was born in 1940. Since 1964 he has worked at the Department of Automatic Control Systems at the Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, where he has supervised 18 PhD students. Since 1986 he has been Full Professor. His research interests include the areas of power system control, decentralized control of large-scale systems, process control and optimization. He is author and coauthor of more than 250 scientific papers.

Danica Rosinov´a(Doc, Ing, PhD), born in 1961, graduated from the Slovak Technical University Bratislava, Faculty of Electrical Engineering in 1985 and obtained PhD degree in 1996. At present she is Associate Professor with the Institute of Control and Industrial Informatics, FEI STU Bratislava. Her field of research includes robust stabilization of discrete-time dynamic systems, control of large scale systems, LMI approach in state-space robust control problems, optimization. She has published her scientific results at several IFAC conferences, in the International Journal of Control, Cybernetics and in other scientific journals in Slovakia and abroad.

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