Differential Passivity based Dynamic Controllers.

In this paper, we develop two passivity based control methods by using variances of passivity techniques; they are applicable for a class of systems for which the standard passivity based controllers may be difficult to design. As a preliminary step, we establish the connections among four relevant passivity concepts, namely differential, incremental, Krasovskii's and shifted passivity properties as follows: differential passivity $\implies$ incremental passivity $\implies$ shifted passivity, and differential passivity $\implies$ Krasovskii's passivity. Then, based on our observations, we provide two novel dynamic controllers based on Krasovskii's and shifted passivity properties.