On the design of Walcott-Zak sliding mode observer

This paper explores the design of Walcott-Zak sliding mode observer (WZSMO) for a class of system satisfying some positive real conditions. A new sufficient and necessary existence condition only involving the original system parameters is proposed to simplify the design of WZSMO. The full freedom degree of the design of nonlinear injection of WZSMO is studied. The fact that the linear feedback can be designed independently is discovered. An optimizing design procedure of the nonlinear injection of SMO is proposed to sub-minimize the control cost of nonlinear injection. At last, a numerical example is presented to illustrate the proposed design procedure.