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Preserving positive realness through discretization. (English) Zbl 1005.93030

Continuous linear systems with positive real transfer functions have desirable stability and realizability properties. The conditions to guarantee that continuous positive realness is preserved under discretization by a standard sampler and zero order hold are investigated here. It is shown that for strictly stable continuous transfer functions, a positive threshold of the input-output transmission gain exists such that the resulting continuous transfer function and the discrete counterpart are both positive real. Critically stable transfer functions with simple complex conjugate pairs of poles on the imaginary axis must fulfill additionally a phase condition for each critically stable pole.

If such a condition does not hold, sometimes a lead or lag compensator can be introduced such that the compensated transfer function is positive real. The propositions derived in the paper are illustrated by two examples.

MSC:
93C55Discrete-time control systems
93D10Popov-type stability of feedback systems
93C05Linear control systems