  The problem of step tracking control with a switching input and without any
continuous-valued inputs is considered. The control objective is to reduce the
number of switchings to a minimal value. This approach finds interesting
applications when switching comprises costs and should be avoided. To solve the
problem, a state dependent switching strategy should be designed and the
resulting closed loop is indeed a hybrid system. Therefore, first we
investigate the conditions on a hybrid system for being the desired solution.
Then, we propose a method for designing the switching strategy such that the
closed loop as a hybrid system solves the problem. The proposed method is
applied to the induction motor control problem which results in relatively
simple and efficient control algorithm. Comparison with the direct torque
control for induction motors show that our method has a superior performance in
reducing the number of mode switches.
