An example on the controllability of perturbed linear control systems
The following linear control system is considered: \( \dot{x}= A(t)x + B(t)u(t)\), where \(t\) ranges over the compact interval \(I\), the state vector function \(x\) is \(n\)-dimensional, the control function \(u\) is \(m\)-dimensional and the coefficients \(A\) and \(B\) are measurable matrix-valued functions of appropriate dimensions. It is also assumed that \(A\) and \(B\) are Lebesgue integrable on \(I\). It is shown that small perturbations with respect to the convergence in measure of the coefficients of \(A\) and \(B\) may (not) affect the complete controllability of this system when \(n \geq 2\) \((n=1)\).
scientific article; zbMATH DE number 1124791