Dissipativity and Feedback Dissipativity Properties of General Nonlinear Discrete-Time Systems

摘要

The dissipativity of single-input single-output discrete-time systems which are nonlinear in the states and the control input is examined. Necessary conditions for the characterization of what is regardedas ( V, s)-dissipative systems are given; in the special case of Quadratic Storage Supply lossless systems, necessary and sufficient conditions are proposed. The results obtained are compared with the ones already existing in the literature for losslessness, passivity and dissipativity cases. Sufficient conditions under which a class of non-affine discrete-time control systems can be rendered dis-sipative are derived. A procedure for dealing with feedback dissipativity and passivation problems is proposed, in addition to the extension of the Energy Shaping plus Damping Injection controller design method for the discrete-time case. A discrete-time model for the DC-to-DC buck converter is used as an example to illustrate the control scheme proposed.