  We study the stability and stabilizability of a continuous-time switched
control system that consists of the time-invariant $n$-dimensional subsystems
\dot{x}=A_ix+B_i(x)u\quad (x\in\mathbb{R}^n, t\in\mathbb{R}_+ \textrm{and}
u\in\mathbb{R}^{m_i}),\qquad \textrm{where} i\in{1,...,N} and a switching
signal $\sigma(\bcdot)\colon\mathbb{R}_+\rightarrow{1,...,N}$ which
orchestrates switching between these subsystems above, where
$A_i\in\mathbb{R}^{n\times n}, n\ge1, N\ge2, m_i\ge1$, and where
$B_i(\bcdot)\colon\mathbb{R}^n\rightarrow\mathbb{R}^{n\times m_i}$ satisfies
the condition $\|B_i(x)\|\le\bbbeta\|x\|\;\forall x\in\mathbb{R}^n$. We show
that, if ${A_1,...,A_N}$ generates a solvable Lie algebra over the field
$\mathbbm{C}$ of complex numbers and there exists an element $\bbA$ in the
convex hull $\mathrm{co}{A_1,...,A_N}$ in $\mathbb{R}^{n\times n}$ such that
the affine system $\dot{x}=\bbA x$ is exponentially stable, then there is a
constant $\bbdelta>0$ for which one can design "sufficiently many"
piecewise-constant switching signals $\sigma(t)$ so that the switching-control
systems \dot{x}(t)=A_{\sigma(t)}x(t)+B_{\sigma(t)}(x(t))u(t),\quad
x(0)\in\mathbb{R}^n\textrm{and} t\in\mathbb{R}_+ are globally exponentially
stable, for any measurable external inputs $u(t)\in\mathbb{R}^{m_{\sigma(t)}}$
with $|u(t)|\le\bbdelta$.
