Discontinuous controller designs for chained system by considering Time Scale Transformation

This paper introduces new design methods of discontinuous controller for chained system. The way of reinterpreting the discontinuous controller including Astolfl´s controller as time state control form (TSCF) with new state transformation is proposed. As this proposed transformation has particular structure, the state regulation is difficult. Therefore, the state regulation condition also is derived. The objective class of discontinuous controller has the problem that large overshoot appears when states converge to the origin depending on the initial state condition. So the main purpose of this paper is improvement of discontinuous controller by designing time scale specifying function. To solve this problem a saturation function is used as time scale specifying function. And the method to modify this type of function by considering set of attraction (SOA) is proposed.