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/observation systems 93D25 Input-output approaches in control theory
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