Several Dissipativity and Passivity Implications in the Linear Discrete-time Setting

Some important features and implications of dissipativity and passivity properties in the discrete-time setting are collected in this paper. These properties are mainly referred to as the stability analysis (feedback stability systems and study of the zero dynamics), the relative degree, the feedback passivity property, and the preservation of passivity under feedback and parallel interconnections. Frequency-domain characteristics are exploited to show some of these properties. The main contribution is the proposal of necessary and sufficient conditions in order to render a multiple-input multiple-output linear discretetime invariant system passive by means of a static-state feedback and using the properties of the relative degree and zero dynamics of the system. A discrete-time model for the DCto-DC buck converter is used as an example to illustrate the passivation scheme proposed. In addition, dissipativity frequency-domain properties are related to some feedback stability criteria.