10 problems

Let $G$ be a discrete-time, linear time-invariant plant in negative feedback with a nonlinearity whose slope is restricted to $[0,k]$. Let $k_{AS}$ be the supremum of the values of…

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…

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 $k\in[\zeta,\varkappa]$,…

Consider robustness analysis using the dissipativity-based results of Theorems and, and compare it with robustness analysis using Theorem with general O'Shea-Zames-Falb multipliers…

The paper constructs integral quadratic constraints (IQCs) with a nontrivial terminal cost for subdifferentials of convex functions, using causal and anti-causal O'Shea-Zames-Falb…

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 a system, and suppose that there is no suitable LTI Zames-Falb multiplier for $G$. LTI Zames-Falb multiplier necessity conjecture. The lack of an LTI Zames-Falb multipli…

Zames–Falb multiplier necessity conjecture. If there is no suitable Zames--Falb multiplier for $G$ and $k$, then there exists a slope-restricted nonlinearity in $[0,k]$ such that t…

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…