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27 December 2001 Frequency domain reduction of linear structured uncertain systems using L2-optimal pole retention
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Proceedings Volume 4563, Sensors and Controls for Intelligent Manufacturing II; (2001) https://doi.org/10.1117/12.452649
Event: Intelligent Systems and Advanced Manufacturing, 2001, Boston, MA, United States
Abstract
This paper presents a method for order reduction of linear structured uncertain systems using L2-optimal pole retention. The four Kharitonov's polynomials associated with the numerators nsI(s),nmI(s) and denominators dsI(s), dmI(s) of the original uncertain system and uncertain reduced model are obtained. By taking all combinations of the nsi(s),nmi(s) and dsj(s),dmj(s) for (i,j=1,2,3,4), respectively, we obtain sixteen Kharitonov's systems and sixteen Kharitonov's reduced models. The L2-optimal sixteen Kharitonov's reduced models retaining a given number of poles of the sixteen Kharitonov's systems are determined in a computationally efficient way. An expression for evaluating the minimum of the impulse response error norm for any choice of retained poles is derived in terms of the sixteen Kharitonov's systems parameters. Then, the corresponding optimal sixteen Kharitonov's reduced models numerators are obtained using an order-recursive procedure. An interesting interpolation property of the sixteen Kharitonov's reduced models is also pointed out. A numerical example is included in order to demonstrate the effectiveness of the proposed method.
© (2001) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
O. Ismail and A. R. Al-Hassan "Frequency domain reduction of linear structured uncertain systems using L2-optimal pole retention", Proc. SPIE 4563, Sensors and Controls for Intelligent Manufacturing II, (27 December 2001); https://doi.org/10.1117/12.452649
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