differential operator

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Related to Differentiation operator: Linear differential operator

differential operator

n
(Mathematics) any operator involving differentiation, such as the mathematical operator del ∇, used in vector analysis, where ∇ = i∂/∂x + j∂/∂y+ k∂/∂z, i, j, and k being unit vectors and ∂/∂x, ∂/∂y, and ∂/∂z the partial derivatives of a function in x, y, and z
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Products of differentiation operator and composition operator on H([[PI].sub.+]) are defined by
where [D.sub.t] : R[[t]] [right arrow] R[[t]] is the formal differentiation operator d/dt.
where the vector z [member of] Z [[subset].bar] [R.sup.n] will be named the state vector of this model, u [member of] U [[subset].bar] [R.sup.m] is the vector of control; elements of matrices F and G are transfer functions (TF) and static nonlinearities, p is the differentiation operator. The term K[rho](p) models the unknown inputs to the actuator and to the dynamic process, the evaluation of the q-dimensional vector function [rho] is considered unknown.
Let D be the differentiation operator, i.e., Df = f', [D.sup.k] f = [f.sup.(k)], k [member of] N and [C.sub.[phi]] the composition operator induced by a nonconstant analytic self-map [phi] of D.