3 problems

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Static-gain conjecture for worst-case convergence rates of Lur'e systems
A Lur'e system has a memoryless nonlinearity $\Delta:{\mathbb{R}}^d\to{\mathbb{R}}^d$ that is sector-bounded in $[k_1,k_2]$ . Its asymptotic convergence rate is considered among all…
Conjectureopencontrol-theory lure-systems optimizationarXiv posted 2 days ago
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Aizerman's conjecture for Lur'e systems
Aizerman's conjecture. For global stability of the equilibrium $x=0$ , it suffices to prove stability for all linear feedback functions $\varphi(y)=ky$ with $k\in[\zeta,\varkappa]$ ,…
Conjectureopenabsolute-stability control-theory lure-systemsarXiv posted 2 days ago
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Kalman conjecture for slope-restricted Lur'e systems
Kalman conjecture. Then the negative-feedback interconnection of the continuous-time (or discrete-time) LTI system $G\sim[A,B,C,0]$ and $c6$ is globally asymptotically stable if…
Conjecturerefutedabsolute-stability kalman-conjecture lure-systemsarXiv posted 2 days ago

Static-gain conjecture for worst-case convergence rates of Lur'e systems