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A complete and convex search for discrete-time noncausal FIR Zames-Falb multipliers

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. Discrete-time Lur’e system.

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A complete and convex search for discrete-time noncausal FIR Zames-Falb multipliers

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  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 UKACC PhD Presentation Showcase

  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 UKACC PhD Presentation Showcase

  3. Overview of results • FIR Zames-Falb, noncausal, convex search, covers both slope restricted and odd slope restricted • Remarkably efficient and improvement on existing literature UKACC PhD Presentation Showcase

  4. Phase equivalence Definition (Willems,1968) Amplitude Amplitude UKACC PhD Presentation Showcase

  5. Numerical results UKACC PhD Presentation Showcase

  6. Computation time UKACC PhD Presentation Showcase

  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 UKACC PhD Presentation Showcase

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