5 problems

Let $G$ be a discrete-time, linear time-invariant plant in negative feedback with a nonlinearity $\phi\in S_{0,k}$. Let $k_{AS}$ be the supremum of the values of $k$ for which the…

Let $G$ be an LTI system, let $k_N$ denote its Nyquist gain, and let $0<k<k_N$. Suppose there is no suitable LTI Zames-Falb multiplier for $G+1/k$. Zames-Falb multiplier equality c…

Let $G$ be a stable transfer function, let $k_N$ be its Nyquist value, and let $\phi$ be a memoryless nonlinearity in $S[0,k]$. Kalman conjecture. The feedback interconnection of…

Consider a feedback system with $G\in\mathbf{RH}_\infty$, and let $c6$ be slope-restricted in $S[0,k]$ and monotonically increasing. The Nyquist plot of the linear part is the plot…

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…