A design of a partial sliding mode controller using duality to linear functional observer

This paper considers a control scheme to control outputs having a dimension less than the dimension of the state variable by using sliding mode controller. Sliding mode controller controlling n-dimensional state variable with r control inputs has a switching hyper plane with n-r dimension. If the control objective is to control outputs having less dimension than the state variable, then the characteristics of the hyper plane could be separated into two characteristics having less order than n-r, and outputs could be controlled faster than the case of order n-r. This paper proposes a design scheme for hyper plane with less order using the duality between the design of a switching hyper plane of a sliding mode controller and the design of a linear functional observer. Also, the controller having stability of closed-loop system is shown to exist.