Robust H2 performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs

Systems and Control Letters

Volumn 56, Issue 2, 2007, Pages 159-166

  Farges, Christophe ^a   Peaucelle, Dimitri ^a   Arzelier, Denis ^a   Daafouz, Jamal ^b  

^a LAAS CNRS   (France)

^b UNIVERSITÉ DE LORRAINE   (France)

Author keywords

H2 performance; Linear periodic discrete time systems; LMI; Parameter dependent Lyapunov functions; Polytopic uncertainty; Quadratic stability; Robust stability

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; LYAPUNOV METHODS; OPTIMIZATION; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS); STABILIZATION; STATE FEEDBACK; UNCERTAIN SYSTEMS;

LINEAR PERIODIC DISCRETE TIME SYSTEMS; LMI; PARAMETER DEPENDENT LYAPUNOV FUNCTIONS; POLYTOPIC UNCERTAINTY; QUADRATIC STABILITY;

LINEAR SYSTEMS;

EID: 33845187894     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2006.08.006     Document Type: Article

References (29)

1. Arzelier D., Peaucelle D., and Farges C. Robust analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs. Conference on Decision and Control (December 2005), Seville, Spain
2. 2 problem for sampled data systems. Systems Control Lett. 19 (1992) 1-12
3. Berg M.C., Amit N., and Powell J.D. Multirate digital control system design. IEEE Trans. Automat. Control 33 12 (1988) 1139-1149
4. Bernussou J., Peres P.L.D., and Geromel J.C. A linear programming oriented procedure for quadratic stabilization of uncertain systems. Systems Control Lett. 13 (1989) 65-72
5. Bittanti S., Bolzern P., and Colaneri P. The extended periodic Lyapunov lemma. Automatica 21 (1985) 603-605
6. Bittanti S., Colaneri P., and De Nicolao G. The Periodic Riccati Equation, The Riccati Equation (1991), Springer, Berlin
7. Bittanti S., and Cuzzola F.A. Periodic active control of vibrations in helicopters: a gain-scheduled multi-objective approach. Control Eng. Practice 10 (2002) 1043-1157
8. Bittanti S., and Lovera M. On the zero dynamics of helicopter rotor loads. European J. Control 2 1 (1996) 57-68
9. P. Bolzern, P. Colaneri, The periodic Lyapunov equation, SIAM J. Matrix Anal. Appl. (1988) 499-512.
10. Cao Y.Y., and Franck P.M. Simultaneous LQ optimal control for periodic discrete-time systems. European J. Control 7 (2001) 514-522
11. Colaneri P. Output stabilization via pole placement of discrete-time linear periodic systems. IEEE Trans. Automat. Control 36 6 (1991) 739-742
12. Colaneri P. Periodic control systems: theoretical aspects. IFAC Workshop on Periodic Control Systems (2004), Yokohama, Japan 25-36
13. F.A. Cuzzola, Filtering and control via LMI optimization, Ph.D. Thesis, Politecnico di Milano, 2000.
14. Daafouz J., and Bernussou J. Parameter-dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties. Systems Control Lett. 43 (2001) 355-359
15. De Oliveira M.C., Geromel J.C., and Hsu L. LMI characterization of structural and robust stability: the discrete-time case. Linear Algebra Appl. 296 (1999) 27-38
16. De Souza C.E., and Trofino A. An LMI approach to stabilization of linear discrete-time periodic systems. Internet. J. Control 73 (2000) 696-709
17. Dullerud G.E., and Glover K. Robust performance of periodic systems. IEEE Trans. Automat. Control 41 8 (1996) 1146-1159
18. 2 sampled-data control for linear uncertain systems. IEEE Trans. Systems, Man Cybernet.-Part B: Cybernet 33 1 (2003) 149-155
19. Kao C.Y., Megretski A., and Jönsson U.T. A cutting plane algorithm for robustness analysis of periodically time-varying systems. IEEE Trans. Automat. Control 46 4 (2001)
20. V. Kapila, W.M. Haddad, Robust controller synthesis for uncertain discrete-time periodic systems, in: American Control Conference, Philadelphia, Pennsylvania, USA, June 1998.
21. Khargonekar P.P., Poola K., and Tannebaum A. Robust control of linear time-invariant plants using periodic compensation. IEEE Trans. Automat. Control 30 (1985) 1088-1096
22. J. Löfberg, Yalmip: yet another LMI parser, August 2001 URL: 〈http://control.ee.ethz.ch/∼joloef/yalmip.php〉.
23. Lovera M. Optimal magnetic momentum control for inertially pointing spacecraft. European J. Control 7 1 (2001) 30-39
24. Moore K.L., Bhattacharyya S.P., and Dahleh M. Capabilities and limitations of multirate control schemes. Automatica 29 (1993) 941-951
25. A. Schubert, Linear optimal periodic position control for elliptical orbits, in: AAS/AIAA Space Flight Mechanics Meeting, Santa Barbara, CA, February 2001, Paper AAS 01-237.
26. A. Schubert, Optimal orbit control for spacecraft on elliptical orbits with atmospheric drag, in: ESA Workshop on "On-Board Autonomy", Noordwijk, The Netherlands, October 2001, Paper AAS 01-237.
27. Skelton R.E., Iwazaki T., and Grigoriadis K. A Unified Algebric Approach to Linear Control Design, Taylor and Francis Series in Systems and Control (1998), Taylor & Francis, London
28. 2 control synthesis for periodic systems, in: American Control Conference, Arlington, June 2001.
29. 2 synthesis for spacecraft attitude control with magnetorquers. J. Guidance Control Dynamics 27 5 (2004) 696-709