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Feedback passivity of nonlinear discrete-time systems with direct input-output link. (English) Zbl 1077.93045
This paper deals with the passification problem for nonlinear, discrete-time systems of the form $$x(k+1)= f(x(k), u(k)),\quad y(k)= h(x(k),u(k)),$$ where $f$ and $h$ are smooth maps vanishing at $x= u= 0$. The main result asserts that if the relative degree of the system is zero and there exist locally passive zero dynamics with a positive definite storage function of class $C^2$, then the system can be rendered passive by applying a regular feedback. The case of affine systems is considered with special attention.

##### MSC:
 93D15 Stabilization of systems by feedback 93C55 Discrete-time control systems 93D25 Input-output approaches to stability of control systems
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##### References:
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