6 problems

Let $\mathcal{R}^{r}_{ref}$, $\mathcal{R}^{r}_{MS}$ and $\mathcal{R}^{r}_{AS}$ denote the reference, mean-square and asymptotic stability regions, respectively, and let the left ha…

Let $W$ be the admissible parameter region for the multistep family, let $\mathcal{S}_{\beta_1,\beta_0}$ be the corresponding stability region, and let … The parameter $m$ is admis…

Let $P_{\beta_1,\beta_0}$ and $\mathcal{S}_{\beta_1,\beta_0}$ denote the stability polynomial and stability region associated with parameters $(\beta_1,\beta_0)$, and let … For a s…

For a fixed $n\geq 1$ and $\varphi\in\left[\frac{\pi}{2},\pi\right]$, define … Here ${\mathcal{S}}_n$ is the absolute stability region associated with the $n$th partial sum of the…

Let $n\geq 2$, let $\Lambda$ be the stability region, and let $\mathcal{S}$ be the unit simplex. Define ellipsoids $\mathcal{E}_I$ and $\mathcal{E}_O$ with center…

Ball-complement outer-bound conjecture. The set $\Lambda_{\rm bc}$ is an outer bound for $\Lambda$, namely