A new technique for the synthesis of optimum switching criteria for higher-order saturating systems is investigated in this paper. Basically, the technique consists of generating a linear switching criterion that is equivalent to the optimum switching criterion for each state of the system. Thus as a trajectory of the system is traced out, the optimum forcing function is determined point by point, resulting in the optimum trajectory for the system. The synthesis procedure has been proved experimentally by simulation of a third-order system on an IBM 797 digital computer.

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