Abstract
This entry discusses an important compromise in feedback design: reconciling the superior performance characteristics of the \(\mathcal{H}_{2}\) optimization criterion, with robustness requirements expressed through induced norms such as \(\mathcal{H}_{\infty }\). The fact that both criteria have frequency-domain characterizations and involve similar state-space machinery motivated many researchers to seek an adequate combination. We review here robust \(\mathcal{H}_{2}\) analysis methods based on convex optimization developed in the 1990s and comment on their implications for controller synthesis.
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Bibliography
Anderson B, Moore JB (1990) Optimal control: linear quadratic methods. Prentice Hall, Englewood Cliffs
Bernstein DS, Haddad WH (1989) LQG control with an \(\mathcal{H}_{\infty }\) performance bound: a Riccati equation approach. IEEE Trans Autom Control 34(3):293–305
Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge
Doyle J (1978) Guaranteed margins for LQG regulators. IEEE Trans Autom Control 23(4):756–757
Doyle J, Zhou K, Glover K, Bodenheimer B (1994) Mixed \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty }\) performance objectives II: optimal control. IEEE Trans Autom Control 39(8):1575–1587
Dullerud GE, Paganini F (2000) A course in robust control theory: a convex approach. Texts in applied mathematics, vol 36. Springer, New York
Feron E (1997) Analysis of robust \(\mathcal{H}_{2}\) performance using multiplier theory. SIAM J Control Optim 35(1):160–177
Khargonekar P, Rotea M (1991) Mixed \(\mathcal{H}_{2}/\mathcal{H}_{\infty }\) control: a convex optimization approach. IEEE Trans Autom Control 36(7):824–837
Oksendal B (1985) Stochastic differential equations. Springer, New York
Paganini F (1999) Convex methods for robust \(\mathcal{H}_{2}\) analysis of continuous time systems. IEEE Trans Autom Control 44(2):239–252
Paganini F, Feron E (1999) LMI methods for robust \(\mathcal{H}_{2}\) analysis: a survey with comparisons. In: El Ghaoui L, Niculescu S (Eds) Recent advances on LMI methods in control. SIAM, Philadelphia
Sánchez-Peña R, Sznaier M (1998) Robust systems theory and applications. Wiley, New York
Scherer C, Gahinet P, Chilali M (1997) Multiobjective output-feedback control via LMI-optimization. IEEE Trans Autom Control 42:896–911
Stoorvogel AA (1993) The robust \(\mathcal{H}_{2}\) control problem: a worst-case design. IEEE Trans Autom Control 38(9):1358–1370
Sznaier M, Rotstein H, Bu J, Sideris A (2000) An exact solution to continuous-time mixed \(\mathcal{H}_{2}/\mathcal{H}_{\infty }\) control problems. IEEE Trans Autom Control 45(11):2095–2101
Sznaier M, Amishima T, Parrilo PA, Tierno J (2002) A convex approach to robust \(\mathcal{H}_{2}\) performance analysis. Automatica 38:957–966
Zhou K, Glover K, Bodenheimer B, Doyle J (1994) Mixed \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty }\) performance objectives I: robust performance analysis. IEEE Trans Autom Control 39(8):1564–1574
Zhou K, Doyle J, Glover K (1996) Robust and optimal control. Prentice Hall, Upper Saddle River
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© 2013 Springer-Verlag London
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Paganini, F. (2013). Robust ℋ 2 Performance in Feedback Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_164-1
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_164-1
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