Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Athans, M.: Optimal control: an introduction to the theory and its applications. McGraw-Hill, New York (1966)
Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics (1994)
Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.A.: State-space solutions to standard H 2 and H ∞ control problems. IEEE Transactions on Automatic Control 34(8), 831–847 (1989)
Finsler, P.: Über das Vorkommen definiter und semi-definiter Formen in Scharen quadratischer Formen. Comentarii Mathematica Helvetici 9, 192–199 (1937)
Gahinet, P., Apkarian, P.: A linear matrix inequality approach to \(\mathcal{H}_\infty\) control. International Journal of Robust and Nonlinear Control 4, 421–448 (1994)
Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M.: LMI Control Toolbox. The Math-Works Inc (1995)
Khalil, H.K.: Nonlinear Systems. Prentice Hall, New Jersey (1996)
Kwakernaak, H., Sivan, R.: Linear Optimal Control Systems. Wiley-Interscience, New York (1972)
Lewis, F.L.: Optimal control. John Wiley and Sons, New York (1986)
Moylan, P., Hill, D.: Stability criteria for large-scale systems. IEEE Transactions on Automatic Control 23, 143–149 (1978)
Nesterov, Y., Nemirovskii, A.: Interior-Point Polynomial Algorithms in Convex Programming. Studies in Applied Mathematics. SIAM, Philadelphia (1993)
Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control: Analysis and Design, 2nd edn. Wiley, Chichester (2005)
Scherer, C.W.: Mixed H 2/H ∞ control for time-varying and linear parametrically-varying systems. International Journal of Robust and Nonlinear Control 6, 929–952 (1996)
Scherer, C.W., Gahinet, P., Chilali, M.: Multi-objective output-feedback control via lmi optimization. IEEE Transactions on Automatic Control 42, 896–911 (1997)
Turner, M.C., Herrmann, G., Postlethwaite, I.: Accounting for uncertainty in antiwindup synthesis (submitted, 2003)
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)
van der Schaft, A.: L2-Gain and Passivity Techniques in Nonlinear Control, 2nd edn. Communications and Control Engineering Series. Springer, Berlin (2000)
Vandenberghe, L., Boyd, S.: Semidefinite programming. SIAM Review 38, 49–95 (1996)
Willems, J.C.: Least stationary optimal control and the algebraic riccati equation. IEEE Transactions on Automatic Control 16(6), 621–634 (1971)
Zhou, K., Doyle, J.C., Glover, K.: Robust and Optimal Control. Prentice Hall, New Jersey (1996)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer London
About this chapter
Cite this chapter
Herrmann, G., Turner, M.C., Postlethwaite, I. (2007). Linear Matrix Inequalities in Control . In: Turner, M.C., Bates, D.G. (eds) Mathematical Methods for Robust and Nonlinear Control. Lecture Notes in Control and Information Sciences, vol 367. Springer, London. https://doi.org/10.1007/978-1-84800-025-4_4
Download citation
DOI: https://doi.org/10.1007/978-1-84800-025-4_4
Publisher Name: Springer, London
Print ISBN: 978-1-84800-024-7
Online ISBN: 978-1-84800-025-4
eBook Packages: EngineeringEngineering (R0)