Abstract
We study in this paper the existence of a feedback for linear differential algebraic equation system such that the closed-loop system is positive and stable. A necessary and sufficient condition for such existence has been established. This result can be used to detect the existence of a state feedback law that makes the linear differential algebraic equation system in closed loop positive and stable.
Highlights
IntroductionWe consider the following linear time invariant differential algebraic equation system:
We consider the following linear time invariant differential algebraic equation system: d dt (Ew (t)) = Fw (t) + Gu (1)w (0) = w0 ∈ Rn, where E, F ∈ Rn×n and G ∈ Rn×m are real constant coefficient matrices
The mathematical model describing these systems must take into account this nonnegativity constraint. This leads to the notion of positive differential algebraic equation system [3]
Summary
We consider the following linear time invariant differential algebraic equation system:. Many variables in these systems involve quantities that are intrinsically nonnegative, such as absolute temperatures, concentration of substances in chemical processes, level of liquids in tanks, and number of proteins These examples belong to the important class of systems which have the property that the state is nonnegative whenever the initial conditions are nonnegative. The mathematical model describing these systems must take into account this nonnegativity constraint This leads to the notion of positive differential algebraic equation system [3]. We present in this short paper a novel approach to detect the existence of a state feedback law that makes the linear differential algebraic equation system in closed loop positive and stable.
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