Discontinuous Controller Design of the Chained Form System via Time State Control Form

This paper introduces a new design method of a discontinuous controller for the chained form system. The proposed method is based on a new Time State Control Form (TSCF) representation of the chained form with a specially designed time scale function. This form can express the Astolfi controller as a special case, and thus enables us to relax the state regulation condition. Using this relaxed condition, one can modify design various kinds of discontinuous controllers. Two application examples are presented. The first one is a performance improvement of the Astolfi controller when |x₁|, which is the denominator of the sigma-process, is large. The improvement is achieved by re-designing the time scale function for the Astolfi controller. The second example deals with the chained system with input constraints. It is shown that the original controller can be modified to satisfy the constraints without narrowing the set of attraction