A Method of Computing Performance Functionals for Linear Dynamical Systems†

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Abstract
The general problem is considered of computing functionals of tho response of linear, constant coefficient dynamical systems of the form where f(t) is any Laplace-transformable function of time and Q(x) any homogeneous algebraic form in the components of a state vector x, A matrix M is introduced, together with a ‘ matrix Laplace transform’ F(M) of f(l). Using these matrices, the class of functional considered may be computed simply in terms of an algebraic form in a set of release coordinates. This enables response functionals of this type to be computed directly in terms of system component values without an intermediate determination of the explicit form of the response.

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