Local feedback dissipativity through energy invariance and feedback losslessness properties in nonlinear discrete-time systems

Sufficient conditions under which a class of nonlinear discrete-time systems which are non-affine in the control input and the states can be rendered locally dissipative are derived. Two methodologies in order to render nonlinear single-input single-output discrete-time systems locally dissipative are given. Dissipativity is seen as a "perturbation'' of the storage energy invariance or the feedback losslessness situations, in the sense that the control which makes the system dissipative is based on the control that makes the storage energy function V invariant or on the control that renders the system lossless. An example is used in order to illustrate the feedback dissipativity methodologies.