1. A complete and convex search for discrete-time noncausal FIR Zames-Falb multipliers
Student: Shuai Wang
Supervisor: William P. Heath
Co-supervisor: Joaquin Carrasco
The University of Manchester
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2. Discrete-time Lur’e system
If an LTI plant G is in negative feedback with an S[0, k] slope-restricted nonlinearity, then stability is guaranteed if there is a multiplier M such that
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Overview of results
Types of methods
Continuous methods
Discrete methods
Finite Impulse Response
Safonov, 1987; Gapski, 1994; Chang, 2012
FIR Zames-Falb
Basis functions
Chen & Wen,1995; Vee,2013
Restricted structure
rational multipliers
Turner,2009; Carrasco,2012; Turner,2011
Ahmad,2013
Jury-Lee criteria &
Lyapunov approach
Khalil2002; Kothare,1999;
Carrasco,2013
Ahmad,2012
FIR Zames-Falb, noncausal, convex search, covers both slope restricted and odd slope restricted
Remarkably efficient and improvement on existing literature
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Phase equivalence
Lemma
Given , if there exists a Zames-Falb multiplier M such that
then there exists an FIR Zames-Falb multiplier MFIR such that
Definition (Willems,1968)
Amplitude
Amplitude
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Numerical results
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Computation time
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7. Conclusion and future work
Phase-equivalence
Discrete-time FIR Zames-Falb multipliers are phase-equivalent to the class of discrete-time rational Zames-Falb multipliers
A convex search for discrete-time Zames-Falb multipliers with FIR structure
KYP lemma derived for discrete-time noncausal transfer functions
No source of conservatism
Complete search and it is expected to be the best for slope-restricted nonlinearities
Future work
MIMO extension
Anti-windup synthesis
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