6 problems

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Exhaustion conjecture for superintegrable discrete-time systems from the $\mathfrak{sl}_{2}(\mathbb{R})$ coalgebra construction
Exhaustion conjecture. The systems obtained by this algebraic construction exhaust the $(super)integrable$ cases associated with $\mathfrak{sl}_{2}(\mathbb{R})$ .
Conjectureopencoalgebra-symmetry discrete-time-systems integrable-systemsarXiv posted 2 days ago
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Zames–Falb multiplier necessity conjecture for discrete-time LTI plants
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…
Conjectureopenabsolute-stability discrete-time-systems zames-falb-multipliersarXiv posted 2 days ago
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Discrete-time off-axis circle criterion conjecture
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…
Conjecturerefutedabsolute-stability circle-criterion discrete-time-systemsarXiv posted 2 days ago
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Discrete-time counterpart conjecture for asymptotic stability of switched systems
Discrete-time counterpart conjecture. The asymptotic stability condition for discrete-time switched systems presented in Knorn, Hespanholo, and Shorten (2014) should also follow fr…
Conjectureopendiscrete-time-systems stability switched-systemsarXiv posted 2 days ago
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Conjecture on positivity-free rank characterizations for singular state matrices
Rank-characterization conjecture. When $A$ is singular, the LMI $$ should have the same solution set as the equation
Conjectureopenall-pass-functions discrete-time-systems linear-matrix-inequalitiesarXiv posted 2 days ago
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Conjecture on Lyapunov representations of observable all-pass functions
Lyapunov representation conjecture. There exists a symmetric matrix $P=P^{\top}$ satisfying
Conjectureopenall-pass-functions discrete-time-systems lyapunov-equationsarXiv posted 2 days ago

6 problems

Exhaustion conjecture for superintegrable discrete-time systems from the sl2(R)\mathfrak{sl}_{2}(\mathbb{R})sl2​(R) coalgebra construction

Zames–Falb multiplier necessity conjecture for discrete-time LTI plants

Discrete-time off-axis circle criterion conjecture

Discrete-time counterpart conjecture for asymptotic stability of switched systems

Conjecture on positivity-free rank characterizations for singular state matrices

Conjecture on Lyapunov representations of observable all-pass functions

Exhaustion conjecture for superintegrable discrete-time systems from the $\mathfrak{sl}_{2}(\mathbb{R})$ coalgebra construction