Minimal discrete - time positive realizations of transfer functionswith positive real polesLuca
نویسندگان
چکیده
A standard result of linear system theory states that a SISO rational n-th order transfer function always has a n-th order realization. In some applications one is interested in having a realization with nonnegative entries (i.e. a positive system). In this paper we give a contribution to the discrete-time realization problem by providing explicit necessary and suucient conditions for a third order transfer function with distinct real positive poles to have a third order positive realization. The conditions are easily testable and the proof is constructive so that it is straighforward to obtain a minimal positive realization.
منابع مشابه
Positive minimal realizations for singular discrete-time systems with delays in state and delays in control
The positive (minimal) realization problem for a class of singular discrete-time linear single-input, single-output systems with delays in state and delays in control is addressed. Solvability conditions for the positive (minimal) realization problem are established. It is shown that there exists a positive (minimal) realization of an improper transfer function T (z) = n(z)/d(z) if the coeffici...
متن کاملRealization problem for positive multivariable continuous-time systems with delays
The realization problem for positive, multivariable continuous-time linear systems with delays in state and in control is formulated and solved. Sufficient conditions for the existence of positive realizations of a given proper transfer function are established. A procedure for computation of positive minimal realizations is presented and illustrated by an example.
متن کاملMinimal Positive Realizations of Transfer Functions with Positive Real Poles
A standard result of linear-system theory states that a SISO rational th-order transfer function always has an th-order realization. In some applications, one is interested in having a realization with nonnegative entries (i.e., a positive system) and it is known that a positive system may not be minimal in the usual sense. In this paper, we give an explicit necessary and sufficient condition f...
متن کاملMinimal eventually positive realizations of externally positive systems
It is a well-know fact that externally positive linear systems may fail to have a minimal positive realization. In order to investigate these cases, we introduce the notion of minimal eventually positive realization, for which the state update matrix becomes positive after a certain power. Eventually positive realizations capture the idea that in the impulse response of an externally positive s...
متن کاملPositive stable realizations of fractional continuous-time linear systems
Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realiz...
متن کامل