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