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The problem of step tracking control with a switching input and without anycontinuous-valued inputs is considered. The control objective is to reduce thenumber of switchings to a minimal value. This approach finds interestingapplications when switching comprises costs and should be avoided. To solve theproblem, a state dependent switching strategy should be designed and theresulting closed loop is indeed a hybrid system. Therefore, first weinvestigate the conditions on a hybrid system for being the desired solution.Then, we propose a method for designing the switching strategy such that theclosed loop as a hybrid system solves the problem. The proposed method isapplied to the induction motor control problem which results in relativelysimple and efficient control algorithm. Comparison with the direct torquecontrol for induction motors show that our method has a superior performance inreducing the number of mode switches.

Minimal Switch Step Tracking Control of Switched Systems with Application to Induction Motor Control