Local stabilization of a linear plant by a pulse signal. (Q556737)

The author considers a control system described by \[ \frac{dx}{dt}=Ax+bf,~\sigma=c^*x,~f=M\sigma, \] where \(A\) is a constant real \(\nu\times\nu\) matrix, \(b\) and \(c\) are constant \(\nu\)-dimensional vector-columns. Using functions of Lyapunov type which are discontinuous with respect to time, two sufficient conditions for the boundedness of all solutions of the system are obtained.