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Linear matrix inequalities in control. (English) Zbl 1327.93180

Turner, Matthew C. (ed.) et al., Mathematical methods for robust and nonlinear control. EPSRC summer school, Leicester, UK, September 2006. London: Springer (ISBN 978-1-84800-024-7/pbk). Lecture Notes in Control and Information Sciences 367, 123-142 (2007).
Summary: This chapter gives an introduction to the use of linear matrix inequalities (LMIs) in control. LMI problems are defined and tools described for transforming matrix inequality problems into a suitable LMI-format for solution. Several examples explain the use of these fundamental tools.
For the entire collection see [Zbl 1125.93003].

MSC:

93B51 Design techniques (robust design, computer-aided design, etc.)
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93B35 Sensitivity (robustness)
93B60 Eigenvalue problems

Software:

LMI toolbox
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Athans, M.: Optimal control: an introduction to the theory and its applications. McGraw-Hill, New York (1966)
[2] Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics (1994) · Zbl 0816.93004
[3] Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.A.: State-space solutions to standard \(H\)_{2} and \(H\)_\infty control problems. IEEE Transactions on Automatic Control 34(8), 831-847 (1989) · Zbl 0698.93031 · doi:10.1109/9.29425
[4] Finsler, P.: Über das Vorkommen definiter und semi-definiter Formen in Scharen quadratischer Formen. Comentarii Mathematica Helvetici 9, 192-199 (1937) · JFM 63.0054.02
[5] Gahinet, P., Apkarian, P.: A linear matrix inequality approach to · Zbl 0808.93024 · doi:10.1002/rnc.4590040403
[6] Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M.: LMI Control Toolbox. The Math-Works Inc (1995)
[7] Khalil, H.K.: Nonlinear Systems. Prentice Hall, New Jersey (1996)
[8] Kwakernaak, H., Sivan, R.: Linear Optimal Control Systems. Wiley-Interscience, New York (1972) · Zbl 0276.93001
[9] Lewis, F.L.: Optimal control. John Wiley and Sons, New York (1986) · Zbl 0665.93065
[10] Moylan, P., Hill, D.: Stability criteria for large-scale systems. IEEE Transactions on Automatic Control 23, 143-149 (1978) · Zbl 0398.93045 · doi:10.1109/TAC.1978.1101721
[11] Nesterov, Y., Nemirovskii, A.: Interior-Point Polynomial Algorithms in Convex Programming. Studies in Applied Mathematics. SIAM, Philadelphia (1993) · Zbl 0824.90112
[12] Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control: Analysis and Design, 2nd edn. Wiley, Chichester (2005) · Zbl 0883.93001
[13] Scherer, C.W.: Mixed \(H\)_{2}/\(H\)_\infty control for time-varying and linear parametrically-varying systems. International Journal of Robust and Nonlinear Control 6, 929-952 (1996) · Zbl 0861.93009 · doi:10.1002/(SICI)1099-1239(199611)6:9/10<929::AID-RNC260>3.0.CO;2-9
[14] Scherer, C.W., Gahinet, P., Chilali, M.: Multi-objective output-feedback control via lmi optimization. IEEE Transactions on Automatic Control 42, 896-911 (1997) · Zbl 0883.93024 · doi:10.1109/9.599969
[15] Turner, M.C., Herrmann, G., Postlethwaite, I.: Accounting for uncertainty in antiwindup synthesis (submitted, 2003)
[16] Turner, M.C., Herrmann, G., Postlethwaite, I.: An introduction to linear matrix inequalities in control. University of Leicester Department of Engineering Techincal Report no 02-04 (2004)
[17] van der Schaft, A.: L2-Gain and Passivity Techniques in Nonlinear Control, 2nd edn. Communications and Control Engineering Series. Springer, Berlin (2000) · Zbl 0937.93020
[18] Vandenberghe, L., Boyd, S.: Semidefinite programming. SIAM Review 38, 49-95 (1996) · Zbl 0845.65023 · doi:10.1137/1038003
[19] Willems, J.C.: Least stationary optimal control and the algebraic riccati equation. IEEE Transactions on Automatic Control 16(6), 621-634 (1971) · doi:10.1109/TAC.1971.1099831
[20] Zhou, K., Doyle, J.C., Glover, K.: Robust and Optimal Control. Prentice Hall, New Jersey (1996) · Zbl 0999.49500
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