On the discretization of switched linear systems

A bilinear single-control system which can be viewed as a control formulation of a linear switched system is considered. The control is restricted to take values either (i) in {0,1}{0,1} (switched system), or (ii) in [0,1][0,1] (relaxed system). In more practical considerations the control is often allowed to change only at the points of a given time-net with a step length hh. The paper investigates what is the approximation error in terms of the reachable set in the two cases (i) and (ii). The error estimates that follow directly from known results are of order h and hh, respectively. In the present paper estimations of order hh and h1.5h1.5 are proved in a constructive way. The second one makes use of the effect of non-accumulation of errors established earlier by the second author.