Abstract
The linear \(\mathcal{H}_{\infty }\)-control theory makes extensive use of transfer functions, which are revised in this chapter. The \(\mathcal{H}_{\infty }\) norm is introduced in the Hardy space of stable transfer matrices, and its optimization is given for linear-controlled plants in terms of two algebraic Riccati equations with a separation structure reminiscent of the classical linear quadratic Gaussian theory. An alternative \(\mathcal{H}_{\infty }\) synthesis, relying on two algebraic Riccati inequalities, is developed for later extension to nonsmooth setting.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aguilar, L., Orlov, Y., Acho, L.: Nonlinear \(\mathcal{H}_{\infty }\)-control of nonsmooth time varying systems with application to friction mechanical manipulators. Automatica 39, 1531–1542 (2003)
Anderson, B., Vreugdenhil, R.: Network Analysis and Synthesis. Prentice Hall, Englewood Cliffs (1973)
Balas, G., Chiang, R., Packard, A., Safonov, M.: Robust Control Toolbox. Version 3. Math Works, Natick, MA (2005)
Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequality in Systems and Control Theory. Studies in Applied Mathematics. SIAM, Philadelphia (1994)
Doyle, J., Glover, K., Khargonekar, P., Francis, B.: State-space solutions to standard \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty }\) control problems. IEEE Trans. Automat. Contr. 34(8), 831–847 (1989)
Gabinet, P., Apkarian, P.: A linear matrix inequality approach to \(\mathcal{H}_{\infty }\) control. Int. J. Robust Nonlinear Control 4(4), 421–448 (1994)
Orlov, Y.: Regularization of singular \(\mathcal{H}_{2}\) and \(\mathcal{H}_{2}\) control problems. In: Proceedings of 36th Conference on Decision and Control, San Diego, pp. 4140–4144 (1997)
Petersen, I.: Disturbance attenuation and \(\mathcal{H}_{\infty }\) optimization: a design method based on the algebraic Riccati equation. IEEE Trans. Automat. Contr. 32, 427–429 (1987)
Safonov, M., Limebeer, D., Chang, R.: Simplifying the \(\mathcal{H}_{\infty }\) theory via loop shifting, matrix pencil, and descriptor concepts. Int. J. Control 50, 2467–2488 (1989)
Shahian, B., Hassul, M.: Control System Design Using MATLAB. Prentice Hall, Englewood Cliffs (1993)
Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control—Analysis and Design. Wiley, Chichester (2005)
Stoorvogel, A., Trextelman, H.: The quadratic matrix inequality insingular \(\mathcal{H}_{\infty }\) control with state feedback. SIAM J. Control Optim. 28, 1190–1208 (1990)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media, New York
About this chapter
Cite this chapter
Orlov, Y.V., Aguilar, L.T. (2014). Linear \(\mathcal{H}_{\infty }\) Control of Autonomous Systems. In: Advanced H∞ Control. Systems & Control: Foundations & Applications. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-0292-7_1
Download citation
DOI: https://doi.org/10.1007/978-1-4939-0292-7_1
Published:
Publisher Name: Birkhäuser, New York, NY
Print ISBN: 978-1-4939-0291-0
Online ISBN: 978-1-4939-0292-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)