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Lur'e problem block diagram. An early nonlinear feedback system analysis problem was formulated by A. I. Lur'e.Control systems described by the Lur'e problem have a forward path that is linear and time-invariant, and a feedback path that contains a memory-less, possibly time-varying, static nonlinearity.
An underdetermined system of linear equations has more unknowns than equations and generally has an infinite number of solutions. The figure below shows such an equation system y = D x {\displaystyle \mathbf {y} =D\mathbf {x} } where we want to find a solution for x {\displaystyle \mathbf {x} } .
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]
In DACs, it is a measure of the deviation between the ideal output value and the actual measured output value for a certain input code. In ADCs, it is the deviation between the ideal input threshold value and the measured threshold level of a certain output code. This measurement is performed after offset and gain errors have been compensated. [1]
The Kalman filter assumes that the measurement errors of the radar, and the errors in its target motion model, and the errors in its state estimate are all zero-mean with known covariance. This means that all of these sources of errors can be represented by a covariance matrix. The mathematics of the Kalman filter is therefore concerned with ...
Differential non-linearity is a measure of the worst-case deviation from the ideal 1 LSB step. For example, a DAC with a 1.5 LSB output change for a 1 LSB digital code change exhibits 1⁄2 LSB differential non-linearity. Differential non-linearity may be expressed in fractional bits or as a percentage of full scale.
The homotopy analysis method (HAM) has also been reported for obtaining approximate solutions of the Duffing equation, also for strong nonlinearity. [ 4 ] [ 5 ] In the special case of the undamped ( δ = 0 {\displaystyle \delta =0} ) and undriven ( γ = 0 {\displaystyle \gamma =0} ) Duffing equation, an exact solution can be obtained using ...
The advantage of this technique is that it results in a simplification of the mathematics; the differential equations that represent the system are replaced by algebraic equations in the frequency domain which is much simpler to solve. However, frequency domain techniques can only be used with linear systems, as mentioned above.