26 problems

Periodic-solution conjecture. If all solutions are uniform-bounded and uniform ultimate-bounded, then there exists a nonzero periodic solution with period $T$, which need not be un…

Continuous-time dissipativity conjecture. Continuous-time counterparts of these discrete-time results should be feasible.

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…

Isolated-barrier conjecture. In the case of nonlinear systems, infinitely many equally spaced isolated barriers should occur.

Consider the globally rationally stable polynomial vector field … and the SOS tests for rational stability applied globally on $\Omega=\mathbb{R}^3$, with fixed gain bound $M=1.5$…

OZF multiplier conjecture. If such a multiplier exists, then $y_2\in\mathcal{L}_2\cap\mathcal{L}_{\infty}$.

Altshuller multiplier conjecture. If such a multiplier exists, then there exists a nonzero periodic solution with period $T$, which need not be unique or attracting.

Lyapunov-type formulation conjecture. The larger entry size and lower cost observed for the Lyapunov-type dynamics arise because the Lyapunov-type formulation effectively encodes t…

Vertex-disjoint path conjecture. In the full measurement case, a DAG is generically identifiable in the class $\mathcal{F}_A$ if and only if there are vertex-disjoint paths from ex…

Let $u$ satisfy the abstract damped wave equation … where $\operatorname{sign}:\mathbb{R}\to\mathcal{P}(\mathbb{R})$ is the set-valued sign function given by…

Aizerman's conjecture. The system is globally asymptotically stable if, for every $k\in[k_1,k_2]$, the linearized system

Lie-algebraic characterization conjecture. Lie-algebraic conditions on $\mathfrak{g}_F$ could be used to characterize uniform stability. This conjecture proposes a Lie-algebraic ap…

A monotone static nonlinearity is a static nonlinearity satisfying the monotonicity condition; a Zames–Falb multiplier is a multiplier of the type used to certify robust stability…

The linearized dynamics are given by $x_{k+1}=A_{\tilde{x}}x_k+Bu_k+e_{\tilde{x}}$, and Assumption 2 requires the existence of $\underline{\sigma}>0$ such that…

Let $\mathbf{f}$ satisfy the assumptions of Theorem, let $\hat{\mathbf{x}}$ be the zero under consideration, and write $\delta_{\hat{\mathbf{x}}}(\mathbf{f})$ for its depth. Let…

Stabilizability conjecture. The system is stabilizable under these growth and polynomial-rule conditions.

Consider incremental affine abstraction of a nonlinear system using sample points in a domain, with a warm-start providing the initial samples. The second issue is that, when using…

Let $\mathcal{R}_1$ be the starting region for an incremental affine abstraction, and consider the issue of conservative approximations caused by constraints that guarantee future…

Sufficient-depth conjecture. The order of $\alpha+1$ layers would be sufficient.

Sufficient-width conjecture. Double layers of such order should be sufficient in other nonlinear systems with other noise levels.

One-switch controllability conjecture. If the smooth target is STLA at $\bar x$, then the target can be reached from every point in a neighborhood of $\bar x$ using a piecewise con…

Let a two-control system be in the particular case where … Here $B_2$ denotes the second obstruction discussed in the paper, and $f_1$, $f_2$, and $R_1$ are the vector fields and b…

Kalman's convergence-rate conjecture. For any stable $G$ and $\Delta\in S[0,K]$ with $K<K_N$,

Model Boundary Approximation Method (MBAM) is a method for approximating models by exploring their parameter-space boundaries. MBAM conjecture. MBAM may provide a framework for the…

A nonlinear system has an equilibrium point $(x_0,u_0)$, and its linearization around that point determines whether the system is locally non-passive: the linearization is non-pass…