19 problems

Let $A_0,A_1\in M_d(\mathbb{R})$ be Metzler matrices defining a linear switched system. A counterexample to the question of whether exponential convergence to zero for all trajecto…

Let $\beta\in\mathbb{R}_{>1}$, let $c$ be the contraction factor associated with $A_2$, and let ${\cal M}(\theta,c,\beta)$ denote the corresponding switched-system matrix family. I…

Let the system be in the mode-independent feedback setting, and let the LMIs associated with a De Bruijn graph of order $l\in\mathbb{N}$ be the conditions used to design stabilizin…

Let $d4a2,d4a2$ be path-complete Lyapunov functions in $d52f\mathrm{pc}(\Sigma)$ satisfying Assumption. Suppose that $d53d$ is a subset of linear invertible maps. The composition-l…

Average-dwell-time stability equivalence conjecture. For every $\tau>0$, System $$ is $\tau\text{-UGB}$ if and only if it is UGAS with respect to $\mathcal{S}_{\mathrm{adw}}(\tau,N…

Input-extension conjecture. The results of this paper can be extended from white-noise inputs to more general inputs, including inputs generated by autoregressive models driven by…

Let a positive linear switched system (PLS) be a switched linear system whose subsystem matrices preserve the positive cone, and let GUAS mean globally uniformly asymptotically sta…

Let $M\in\mathbb{Z}^{+}$ and let … Suppose that the switched system under consideration is robust feedback stabilizable. Non-conservatism conjecture. There exists an…

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…

State-dependent switching conjecture. Such an assumption could render the average dwell-time Assumption unnecessary.

Continuous-time irregular growth conjecture. There exist integers $k,d\geq1$ and matrices $A_1,\ldots,A_k\in M_d(\mathbb{R})$ such that, for every unit vector $u\in\mathbb{R}^d$ an…

Let $\mathsf{A}$ be a discrete-time linear switched system whose diagonal blocks $A_k^{(i,i)}$ are fixed, and let the off-diagonal blocks $A^{(i,j)}$ vary freely. Write…

Discrete-time counterpart conjecture. The asymptotic stability condition for discrete-time switched systems presented in Knorn, Hespanholo, and Shorten (2014) should also follow fr…

Common-left-eigenvector convergence conjecture. If the matrices $C(t_k)$, $k\geq 0$, have a common left eigenvector corresponding to the eigenvalue one, then the state of system co…

Mason–Shorten–Angeli conjecture. If the system is a positive linear switched system, then this Hurwitz condition is sufficient for global uniform asymptotic stability.

Lower Lyapunov exponent conjecture. The lower Lyapunov exponent of the system is the spectral abscissa $\sigma(A_2)$. This conjecture is suggested by the numerical computations in…

Let $A$ be a matrix that can be put in block cyclic permutation form in some basis, and let $b$ have one or more zero blocks in that basis. If $Z$ is the set of indices of the zero…

Mode-wise contraction conjecture. For certain classes of piecewise-smooth systems, contraction of each individual mode should be sufficient to guarantee convergence of all system t…

Let $\boldsymbol{S}=\{S_1,S_2\}\subset\mathbb{R}^{d\times d}$, with $d\geq 4$, be an arbitrary pair satisfying condition (1.3a), namely that the matrices share a common non-strict…