H2 and H00 design of sampled-data systems using lifting. Part I: General framework and solutions

SIAM Journal on Control and Optimization

Volumn 38, Issue 1, 2000, Pages 175-196

  Mirkin, Leonid ^a   Rotstein, Hector P ^a   Palmor, Zalman J ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

f2 optimization; Generalized sampler and hold; H optimization; Lifting technique; Sampled data control

Indexed keywords

CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; DISCRETE TIME CONTROL SYSTEMS; OPTIMAL CONTROL SYSTEMS;

LIFTING TECHNIQUES;

SAMPLED DATA CONTROL SYSTEMS;

EID: 0343789028     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0363012997329603     Document Type: Article

References (32)

1. M. ARAKI, Recent developments in digital control theory, in Proceedings of 12th IFAC Word Congress, vol. IX, Sydney, Australia, 1993, pp. 251-260.
2. B. BAMIEH, Optimal samplers and optimal hold functions in sampled-data problems, in Proceedings of 3rd IEEE Mediterranean Symposium on New Directions in Control and Automation, vol. 2, 1995, Limassol, Cyprus, pp. 63-68.
3. B. BAMIEH AND J. B. PEARSON, A general framework for linear periodic systems with applications to H°° sampled-data control, IEEE Trans. Automat. Control, 37 (1992), pp. 418-435.
4. B. BAMIEH AND J. B. PEARSON, The H2 problem for sampled-data systems, Systems Control Lett., 19 (1992), pp. 1-12.
5. B. BAMIEH, J. B. PEARSON, B. A. FRANCIS, AND A. TANNENBAUM, A lifting technique fo linear periodic systems with applications to sampled-data control, Systems Control Lett. 17 (1991), pp. 79-88.
6. [C] T. BAS.AR, Optimum H°° designs under sampled state measurements, Systems Control Lett. 16 (1991), pp. 399-409.
7. J. H. BRASLAVSKY, Frequency Domain Analysis of Sampled-data Control Systems, Ph.D. thesis Department of Electrical and Computer Eng., The University of Newcastle, Newcastle Australia, 1995.
8. T. CHEN AND B. A. FRANCIS, Optimal Sampled-Data Control Systems, Springer-Verlag, London, 1995.
9. P. COLANERI, Hamiltonian matrices for lifted systems and periodic Riccati equations i H2/H°° analysis and control, in Proceedings of the 30th IEEE Conference on Decisio and Control, vol. 2, Brighton, UK, 1991, pp. 1914-1919.
10. A. FEUER AND G. C. GOODWIN, Generalized sample hold function: Frequency domain analysi of robustness, sensitivity and intersample difficulties, IEEE Trans. Automat. Control, 39 (1994), pp. 1042-1045.
11. G. Gu, J. ClIEN, AND O. TOKER, Computation of L2[0,h] induced norms, in Proceedings o the 35th IEEE Conference on Decision and Control, Kobe, Japan, 1996, pp. 4046-4051.
12. E. S. HAMBY, Y.-C. JUAN, AND P. T. KABAMBA, Optimal hold functions for digital contro systems, in Control and Dynamic Systems, C. T. Leondes, ed., vol. 79, Academic Press 1996, pp. 1-50.
13. V. lONESCU AND M. WEISS, Continuous and discrete-time Riccati theory: A Popov-functio approach, Linear Algebra and its Applications, 193 (1993), pp. 173-209. [
14. Y.-C. JUAN AND P. T. KABAMBA, Optimal hold functions for sampled data regulation, Auto matica, 27 (1991), pp. 177-181.
15. P. T. KABAMBA, Control of linear systems using generalized sampled-data hold functions, IEE Trans. Automat. Control, 32 (1987), pp. 772-783.
16. P. T. KABAMBA AND S. KARA, Worst-case analysis and design of sampled-data control systems IEEE Trans. Automat. Control, 38 (1993), pp. 1337-1357.
17. P. P. KHARGONEKAR AND N. SIVASHANKAR, H2 optimal control for sampled-data systems Systems Control Lett., 17 (1991), pp. 425-436.
18. H. KWAKERNAAK AND R. SlVAN, Linear Optimal Control Systems, Wiley & Sons, NY, 1972.
19. L. MIRKIN, On discrete-time H°° problem with a strictly proper controller, Internat. J. Control 66 (1997), pp. 747-765.
20. L. MIRKIN AND Z. J. PALMOR, Mixed discrete/continuous specifications in sampled-data H2 optimal control, Automatica, 33 (1997), pp. 1997-2014.
21. L. MIRKIN AND Z. J. PALMOR, A new representation of the parameters of lifted systems, IEE Trans. Automat. Control, 44 (1999), pp. 833-840.
22. L. MlRKIN AND H. ROTSTEIN, On the characterization of sampled-data controllers in the lifte domain, Systems Control Lett., 29 (1997), pp. 269-277.
23. L. MIRKIN, H. ROTSTEIN, AND Z. J. PALMOR, H2 and /f°° design of sampled-data system using lifting. Part II: Properties of systems in the lifted domain, SIAM J. Control Optim. 38 (1999), pp. 197-218.
24. H. P. ROTSTEIN, Constrained H°°-Optimization for Discrete-Time Control, Ph.D. thesis, California Institute of Technology, Pasadena, CA, 1992.
25. N. SIVASHANKAR AND P. P. KHARGONEKAR, Characterization of the L2-induced norm for linea systems with jumps with applications to sampled-data systems, SIAM J. Control Optim. 32 (1994), pp. 1128-1150.
26. W. SUN, K. M. NAGPAL, AND P. P. KHARGONEKAR, H°° control and filtering for sampled-dat systems, IEEE Trans. Automat. Control, 38 (1993), pp. 1162-1174.
27. G. TADMOR, H°° optimal sampled-data control in continuous-time systems, Internat. J. Control, 56 (1992), pp. 99-141.
28. H. T. TOIVONEN, Sampled-data control of continuous-time systems with an H°° optimalit criterion, Automatica, 28 (1992), pp. 45-54.
29. H. T. TOIVONEN, Digital control with H°° optimality criteria, in Control and Dynamic Systems C. T. Leondes, ed., Academic Press, 71 (1995), pp. 215-262.
30. H. L. TRENTELMAN AND A. A. STOORVOGEL, Sampled-data and discrete-time H2 optimal control, SIAM J. Control Optim., 33 (1995), pp. 834-862.
31. Y. YAMAMOTO, A function space approach to sampled data control systems and tracking problems, IEEE Trans. Automat. Control, 39 (1994), pp. 703-713.
32. K. ZHOU, J. C. DOYLE, AND K. GLOVER, Robust and Optimal Control, Prentice-Hall, Engle wood Cliffs, NJ, 1995.