  We study the bifurcation of limit cycles from the periodic orbits of
$2n$--dimensional linear centers $\dot{x} = A_0 x$ when they are perturbed
inside classes of continuous and discontinuous piecewise linear differential
systems of control theory of the form $\dot{x} = A_0 x + \varepsilon \big(A x +
\phi(x_1) b\big)$, where $\phi$ is a continuous or discontinuous piecewise
linear function, $A_0$ is a $2n\times 2n$ matrix with only purely imaginary
eigenvalues, $\varepsilon$ is a small parameter, $A$ is an arbitrary $2n\times
2n$ matrix, and $b$ is an arbitrary vector of $\mathbb{R}^n$.
