Abstract
In this chapter, we derive explicit controller parametrizations for the design of output feedback controllers for affine Linear Parametrically Varying (LPV) systems in the form of Linear Matrix Inequalities (LMIs). The main feature is that variables related to the LPV controller parameters are retained in the design inequalities, a fact that can be used to impose a simpler structure to the resulting controller as well as to develop applications in a number of control problems, such as mixed objective control problems and delay systems. We develop formulas using two approaches: one based on polytopes and another based on norm-bounded uncertainty models. We provide a comparison between these two approaches and their relation to existing results in the literature.
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References
Apkarian P, Gahinet P (1995) A convex characterization of gain-scheduled h-infinity controllers. IEEE Trans Automat Contr 40(5):853–864
Apkarian P, Gahinet P, Becker G (1995) Self-scheduled H ∞ control of linear parameter-varying systems—a design example. Automatica 31(9):1251–1261
Barmish BR (1985) Necessary and sufficient conditions for quadratic stabilizability of an uncertain system. J Optim Theory Applicat 46:399–408
Becker G, Packard A (1994) Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback. Syst Contr Lett 23(3):205–215
Boyd SP, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadelphia, PA
Fans MKH, Tits AL, Doyle JC (1991) Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics. IEEE Trans Automat Contr 36(1):25–38
Geromel JC, Bernussou J, de Oliveira MC (1999) H 2 norm optimization with constrained dynamic output feedback controllers: decentralized and reliable control. IEEE Trans Automat Contr 44(7):1449–1454
de Oliveira MC, Geromel JC (2004) Synthesis of nonrational controllers for linear delay-systems. Automatica 40(2):171–181
de Oliveira MC, Geromel JC, Bernussou J (2000) Design of dynamic output feedback decentralized controllers via a separation procedure. Int J Contr 73(5):371–381
de Oliveira MC, Geromel JC, Bernussou J (2002) Extended H 2 and H ∞ norm characterizations and controller parametrizations for discrete-time systems. Int J Contr 75(9):666–679
Packard A (1994) Gain scheduling via linear fractional transformations. Syst Contr Lett 22(2):79–92
Scherer CW (2000) Robust mixed control and linear parameter-varying control with full block scalings. In: El Gahoui L, Niculesco SL (eds) Advances in linear matrix inequality methods in control, SIAM, Philadelphia, PA, pp 187–207
Scherer CW (2001) LPV control and full block multipliers. Automatica 37(3):361–375
Scherer CW, Gahinet P, Chilali M (1997) Multiobjective output-feedback control via LMI optimization. IEEE Trans Automat Contr 42(7):896–911
Scorletti G, EL Ghaoui L (1998) Improved LMI conditions for gain scheduling and related control problems. Int J Robust Nonlin Contr 8(10):845–877
Skelton RE, Iwasaki T, Grigoriadis K (1998) A unified algebraic approach to control design. Taylor & Francis, London, UK
Zhou K, Doyle JC, Glover K (1996) Robust and optimal control. Prentice Hall, Inc., Englewood Cliffs, NJ
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de Oliveira, M.C. (2012). Explicit Controller Parametrizations for Linear Parameter-Varying Affine Systems Using Linear Matrix Inequalities. In: Mohammadpour, J., Scherer, C. (eds) Control of Linear Parameter Varying Systems with Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1833-7_4
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DOI: https://doi.org/10.1007/978-1-4614-1833-7_4
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