Consider the following differential equations with initial conditions at time $t_0$ specified:
$\dot{x}_1 = f_1(x_1,t) ; \,\,\,x_1: [t_0,T]\to\mathbb{R}^n, f_1:\mathbb{R}^n\times[t_0,T]\to\mathbb{R}^n \\ \vdots \\$ $\dot{x}_k = f_k(x_k,t); \,\,\,x_1: [t_0,T]\to\mathbb{R}^n, f_1:\mathbb{R}^n\times[t_0,T]\to\mathbb{R}^n \\$
Let $C(p,t)$ denote the convex hull of $\{f_1(p,t), f_2(p,t),...,f_k(p,t) \}$, where $p\in\mathbb{R}^n,t\in[t_0,T] $
Let $C_t(t)$ denote the convex hull of trajectories, that is, the convex hull of $\{x_1(t),...x_k(t)\} $
Then every solution $z(t)$ to the differential inclusion:
$\dot{y}(t) \in C(y,t); \,\,\, y: [t_0,T]\to\mathbb{R}^n$
satisfies the following property: If $z(t_0)\in C_t(t_0)$, then $z(t)\in C_t(t)\forall t \in[t_0,T]$