Exact(5)
And so what we're left with, when we track this through, is that, with a complex exponential input, we get an output which is the same complex exponential, namely this factor, times this integral.
A numerical example for an exponential input gives comparisons of the transient response for the approximate closed form and series Green's function solutions.
The proposed method that changes the initial input response into a shapeable MPPT algorithm is designed based on an exponential input function.
Just to illustrate one additional step in both evaluating inverse transforms and using Fourier transform properties to solve linear constant coefficient differential equations, let's take the same example and, rather than finding the impulse response, let's find the response to another exponential input.
The rate of release from the lung (R t)) of the sequestered propofol after the bolus input is described by: (11) R bolus (t) = (1/ T) Dose frdose exp(- t / T) This sequestration was incorporated into the PBPK model simply by dividing the bolus input into two non-sequestered components: 1) A bolus input of Dose × (1-frdose); and 2) An exponential input of total amount = Dose × frdose.
Similar(55)
Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs.
Sufficient conditions for the exponential input-to-state stability in probability in r th mean and for the almost sure exponential input-to-state stability in probability of a composite stochastic system are established.
We have developed the exponential input-to-state stability in probability of a larger class of multi-input composite system (15).
The purpose of the paper is to fill the gaps in the literature by studying the exponential input-to-state stability in probability in r th mean (REISSP) and the almost sure exponential input-to-state stability in probability (AEISSP) of a CSCS.
Among them, the method of exponential inputs specifically chosen for calculating Volterra kernel in this paper.
One strong argument in favor of exponential inputs is that the limit of a binomial distribution with small probability of success (e.g. entering the system) and defined over a large set of elements or individuals (population) is Poisson.
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Justyna Jupowicz-Kozak
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