zbMATH — the first resource for mathematics

\(\mathcal L_2\) and \(\mathcal H_2\) performance analysis and gain-scheduling synthesis for parameter-dependent systems. (English) Zbl 1283.93121
Summary: This paper focuses on quadratic performance analysis and output feedback gain-scheduling synthesis for parameter-dependent systems with linear fractional representations (LFRs). New quadratic \(\mathcal H_{2}\) and \(\mathcal L_2\) performance analysis results based on full-block multipliers are given. A novel gain-scheduling output feedback synthesis, which can be regarded as a natural extension of the loop shaping design procedure of McFarlane and Glover to parameter-dependent systems, is proposed. This gain-scheduling technique is computationally attractive and yields a simple and transparent control structure that can be easily implemented. Its effectiveness is illustrated on a benchmark missile autopilot example.

93B50 Synthesis problems
93C15 Control/observation systems governed by ordinary differential equations
93C05 Linear systems in control theory
PDF BibTeX Cite
Full Text: DOI
[1] Apkarian, P.; Gahinet, P., A convex characterization of gain-scheduled \(\mathcal{H}_\infty\) controllers, IEEE transactions on automatic control, 40, 5, 853-864, (1995) · Zbl 0826.93028
[2] Apkarian, P.; Adams, R.J., Advanced gain-scheduling techniques for uncertain systems, IEEE transactions on control systems technology, 6, 1, 21-32, (1998)
[3] Barbosa, K.A., Robust \(\mathcal{H}_2\) filtering for uncertain linear systems: LMI based methods with parametric Lyapunov functions, Systems & control letters, 54, 251-262, (2005) · Zbl 1129.93533
[4] Becker, G.; Packard, A., Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback, Systems & control letters, 23, 3, 205-215, (1994) · Zbl 0815.93034
[5] Boyd, S., Linear matrix inequalities in system and control theory, (1994), SIAM Studies in Applied Mathematics Philadelphia, PA
[6] Boyd, S., & Yang, Q. (2001). Structured and simultaneous Lyapunov functions for system stability problems. Stanford University Report · Zbl 0683.93057
[7] Döll, C., A robust self-scheduled missile autopilot: design by multi-model eigenstructure assignment, Control engineering practice, 9, 1076-1078, (2001)
[8] El Ghaoui, L.; Scorletti, G., Control of rational systems using linear-fractional representations and linear matrix inequalities, Automatica, 32, 9, 1273-1284, (1996) · Zbl 0857.93040
[9] Jung, M.; Glover, K., Calibratable linear parameter-varying control of a turbocharged diesel engine, IEEE transactions on control systems technology, 14, 1, 45-62, (2006)
[10] Magni, J.F. (2004). Linear fractional representation toolbox modelling, order reduction, gain scheduling. Technical Report, TR 6/08162 DCSD
[11] McFarlane, D.C.; Glover, K., A loop shaping design procedure using \(H_\infty\) synthesis, IEEE transactions on automatic control, 37, 6, 759-769, (1992) · Zbl 0755.93019
[12] Megretski, A.; Rantzer, A., System analysis via integral quadratic constraints, IEEE transactions on automatic control, 42, 6, 819-830, (1997) · Zbl 0881.93062
[13] Nichols, R.A., Gain scheduling for H-infinity controllers: A flight control example, IEEE transactions on control systems technology, 1, 2, 69-79, (1993)
[14] Packard, A., Gain scheduling via linear fractional transformations, Systems & control letters, 22, 3, 79-92, (1994) · Zbl 0792.93043
[15] Prempain, E. (2006). On coprime factorizations for parameter-dependent systems. In Proceedings of the 45th IEEE conference on decision and control
[16] Rugh, W.J.; Shamma, J.S., Research on gain scheduling, Automatica, 36, 1401-1425, (2000) · Zbl 0976.93002
[17] Scherer, C., Multiobjective output-feedback control via LMI optimization, IEEE transactions on automatic control, 42, 7, 896-911, (1997) · Zbl 0883.93024
[18] Scherer, C.W., LPV control and full block multipliers, Automatica, 37, 361-375, (2001) · Zbl 0982.93060
[19] Scherer, C.W. (2003). LMI relaxations in robust control…How to reduce conservatism. Plenary talk, 4th IFAC symposium on robust control design
[20] Skogestad, S.; Postlethwaite, I., Multivariable feedback control - analysis and design, (2005), J. Wiley & Sons · Zbl 0842.93024
[21] Sun, K.; Packard, A., Robust \(H_2\) and \(H_\infty\) filters for uncertain LFT systems, IEEE transactions on automatic control, 50, 5, 715-720, (2005) · Zbl 1365.93515
[22] Wang, F.; Balakrishnan, V., Improved stability analysis and gain-scheduled controller synthesis for parameter-dependent systems, IEEE transactions on automatic control, 47, 5, 720-734, (2002) · Zbl 1364.93582
[23] Wu, F.; Dong, K., Gain-scheduling control of LFT systems using parameter-dependent Lyapunov functions, Automatica, 42, 39-50, (2006) · Zbl 1121.93067
[24] Zhou, K., Robust and optimal control, (1995), Prentice-Hall International, Inc
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.