Abstract
This chapter is concerned with the problem of robust non-fragile ℌ2 controller design for linear time-invariant discrete time systems with uncertainty. The controller to be designed is assumed to have additive gain variations or multiplicative gain variations, which are due to the finite word-length (FWL) effects when the controller is implemented. Sufficient conditions for the robust non-fragile control problem are given in terms of solutions to a set of matrix inequalities. The resulting design is such that the closed-loop system is robustly stable and has an ℌ2 cost bound against plant uncertainty and controller gain variations. Iterative linear matrix inequalities (LMI) based algorithms are developed. Numerical examples are given to illustrate the design methods.
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References
Ackerman, J.Sampled-Data Control SystemsSpringer-Verlag: Berlin, 1985.
Astrom, K.J. and B. WittenmarkComputer Controlled SystemsPrentice Hall: Upper Saddle River, N.J., 1997.
Basar, T. and P. BernhardH.-Optimal Control and Related Minimax Design Problems: A Dynamic Game ApproachBirkhauser: Boston, Massachusetts, 1991.
Blanchini, F., R.Lo Cigno and R. Tempo, “Control of ATM networks• fragility and robustness issues”Proc. American Control ConferencePhiladephia, Pennsylvania, pp. 2947–2851, 1998.
Boyd, S., L. El Ghaoui, E. Feron and V. BalakrishanLinear Matrix Inequalitiesin Systems and Control Theory,SIAM: Philadelphia, PA, 1994.
Corrado, J.R. and W.M. Haddad, “Static output feedback controllers for systems with parametric uncertainty and controller gain variation”Proc.American Control Conference, San Diego, California, pp. 915–919, 1999.
Dorato, P., “Non-fragile controller design, an overview”Proc. American Control ConferencePhiladephia, Pennsylvania, pp. 2829–2831, 1998.
Doyle, J.C., K. Glover, P.P. Khargonekar and B.A. Francis, “State space solutions to standard H2 andH oe control problems,“IEEE Trans. Automatic Contr., Vol. 34, no. 8, pp. 831–847, 1989.
El Ghaoui, L., F. Oustry, and M. AitRami, “A cone complementarity linearization algorithm for static output feedback and related problems,”IEEE Trans. Automatic Contr.Vol. 42, no. 8, pp. 1171–1176, 1997.
Famularo, D., C.T. Abdallah, A. Jadbabais, P. Dorato, and W.M. Haddad, “Robust non-fragile LQ controllers: the static state feedback case”Proc.American Control Conference, Philadephia, Pennsylvania, pp. 1109–1113, 1998.
Gahinet, P., A. Nemirovski, A.J. Laub, and M. Chilali, LMI Control Toolbox, Natick, MA: The MathWorks, 1995.
Gevers, M. and G. LiParametrization in Control Estimation and Filtering Problem: Accuracy AspectsSpringer-Verlag: Berlin, 1993.
Green, M. and D.J.N. LimebeerLinear Robust ControlPrentice-Hall: Englewood Cliffs, New Jersey, 1995.
Haddad, W.M. and J.R. Corrado, “Resilient controller design via quadratic Lyapunov bounds”Proc. IEEE Conf. Dec. Contr.San Diego, CA, pp. 2678–2683, 1997.
Haddad, W.M. and J.R. Corrado, “Robust resilient dynamic controllers for systems with parametric uncertainty and controller gain variations”Proc. American Control ConferencePhiladephia, Pennsylvania, pp. 2837–2841, 1998.
Jadbabaie, A., T. Chaouki, D. Famularo, and P. Dorato, “Robust, non-fragile and optimal controller design via linear matrix inequalities”Proc. American Control ConferencePhiladephia, Pennsylvania, pp. 2842–2846, 1998.
Kaesbauer, D. and J. Ackermann, “How to escape from the fragility trap”Proc. American Control ConferencePhiladephia, Pennsylvania, pp. 2832–2836, 1998.
Keel, L.H. and S.P. Bhattacharyya, “Stability margins and digital implementation of controllers”Proc.American Control Conference, Philadephia, Pennsylvania, pp. 2852–2856, 1998.
Keel, L.H. and S.P. Bhattacharyya, “Robust, fragile, or optimal?”IEEE Trans. Automatic Contr.Vol. 42, no. 8, pp. 1098–1105, 1997.
Keel, L.H. and S.P. Bhattacharyya, “Authors’ Reply to Comments on ”Robust, Fragile, or Optimal?“IEEE Trans. Automatic Contr.Vol. 43, no. 9, pp. 1268, 1998.
Li, G., “On the structure of digital controllers with finite word length consideration”IEEE Trans. Automatic Contr.Vol. 43, pp. 689–693, 1998.
Makila P.M., “Comments on ”Robust, Fragile, or Optimal?“IEEE Trans. Automatic Contr.Vol. 43, no. 9, pp. 1265–1268, 1998.
Masubuchi, I., A. Ohara and N. Suda, “LMI-based controller synthesis: a unified formulation and solution”Int. J. Robust Nonlinear Controlvol. 8, pp. 669–686, 1998.
Whidborne, J. F., J. Wu and R. S. H. Istepanian, “Finite word length stability issues in an ti framework”Int. J. Controlvol. 73, no. 2, pp. 166–176, 2000.
Yang, G.-H., J.L. Wang, and C. Lin“H oo control for linear systmes with additive controller gain variations“Int. J. Control, vol. 73, no. 16, pp. 1500–1506, 2000.
Yang, G.-H. and J.L. Wang, “Robust non-fragile Kalman filtering for uncertain linear systems with estimator gain uncertainty”IEEE Trans. Automatic Contr.Vol. 46, no. 2, pp. 343–348, 2001.
Yang, G.-H. and J.L. Wang, “Non-fragileH 0 control for linear systems with multiplicative controller gain variations“AutomaticaVol. 37; no. 5; pp. 727–737, 2001.
Zhou, K., J.C. Doyle, and K. GloverRobust Optimal ControlPrentice Hall: Englewood Cliffs, NJ, 1996.
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Yang, GH., Wang, J.L., Soh, Y.C. (2001). Robust Non-Fragile Controller Design for Discrete Time Systems with FWL Consideration. In: Istepanian, R.S.H., Whidborne, J.F. (eds) Digital Controller Implementation and Fragility. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-0265-6_12
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DOI: https://doi.org/10.1007/978-1-4471-0265-6_12
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