Input-response systems

The convolution linear operator met in linear input-response systems (Theorem 16.5) is of great importance in LSA and is encountered in many different contexts. This linear operator consists of a kernel function, g t), and a specific integration operation. 

The relationship between R2 and R is unique and independent of the input. The relationship is independent of the input in the sense that it does not depend on the rate or extent of the input. However, as for any input-response system, the relationship depends on the site of the input. Thus, as long as the drug disposition does not change (time-invariant disposition) and the drug enters the system through the same input site, the relationship between the responses remains unchanged. The 7 i, R2 relationship is a linear operational relationship. In its simplest form it can be a simple convolution-type relationship otherwise it involves additional linear operations (see examples below). The relationship applies to any two PK responses in a multivariate PK system with a linear disposition and, as such, is an alternative to the traditional linear compartmental multivariate analysis. Perhaps the biggest power of the... 

Molecular/Probability Basis of the Convoeution Relationship IN Linear Input-Response Systems... 

FIGURE 16.6 Illustration of linear input-response system. 

The UIR function is also commonly denoted the characteristic function. This is an appropriate notation since it is a function that is characteristic for the given input-response system. In engineering, the Laplace transform of the unit impulse response is commonly called the transfer function. The above equations for x t) and c(0 can be written ... 

The dynamic behavior of the cyclic enzyme system display catastrophic behavior in response to specific changes in external input. The system can realize a neuronic model capable of storing memory. 

The manipulated variable (system input) response is recorded to provide good visibility on both the amplitude and time scales. 

Stability The stability of a system is determined by its response to inputs. A stable system remains stable unless it is excited by an external source, and it should return to its original state once the perturbation is removed and the system cannot supply power to the output irrespective of the input. The system is stable if its response to the impulse excitation approaches 0 at long times or when every bounded input produces a bounded output. Mathematically this means that the function does not have any singularities that caimot be avoided. The impedance Z(s) must satisfy the following conditions Z s) is real when s is real (that is, when 0) and Re[Z(5)] > 0 when v > 0 [ = v -i- ja>, see Section... 

The system is disturbed by a stimulus and the response of the system to the stimulus is measured. Two common stimulus response techniques are the step input response and the pulse input response see Fig. 11.20. 

The most important inputs are those concerning the emergency response systems in place, community types and population densities. General information on population and types of communities may be obtained from census data, and county and state records offices. Detailed information may only be available by... 

If the impulse response function g(x) of a system is known, the output signal y(x) of the system is given for any input signal u(x). The integral equation, which is called superposition integral. 

The step response function h(x) is the response of a system to an unit step s(x) at the input. 

The equation system of eq.(6) can be used to find the input signal (for example a crack) corresponding to a measured output and a known impulse response of a system as well. This way gives a possibility to solve different inverse problems of the non-destructive eddy-current testing. Further developments will be shown the solving of eq.(6) by special numerical operations, like Gauss-Seidel-Method [4]. 

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