# time-invariant system

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## time-invariant system

[′tīm in‚ver·ē·ənt ‚sis·təm]
(control systems)
A system in which all quantities governing the system's behavior remain constant with time, so that the system's response to a given input does not depend on the time it is applied.
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The difference which makes this extension non-obvious is that a time-invariant system is described by two non-commutative polynomials while a time-varying system requires three polynomials, and the third one has to be incorporated into the analysis.
Example 1: Time-Invariant System. Consider a three-output two-input discrete-time Linear Time-Invariant (LTI) system:
(iv) [??] [member of] {PR} denotes that the transfer matrix [??](s) of a linear time-invariant system is positive real; that is, [??](s) + [[??].sup.T] (-s) [greater than or equal to] 0 for all Re s > 0, and [??] [member of] {SPR} denotes that it is strictly positive real; that is, [??](s) + [[??].sup.T](-s) > 0 for all Re s [greater than or equal to] 0.
The parameter matrix [theta] may be thus estimated by means of time-invariant system identification techniques, while the time-dependent AR and MA parameter matrices [A.sub.i] [i] and [C.sub.i] [i] maybe subsequently estimated by using (6), after substituting [theta] by the obtained estimate [??].
In the linear time-invariant system was studied with an ideal uniform sampler  Equations
The observability of a linearized time-invariant system has extensively been studied in many early research works [8, 9].
Reference  reviews the precise integration method; it is not only used to solve time-invariant system, but also for time-variant, nonlinear system, and two-point boundary value problems.
Equations (1), (2), (3), (4), (5), and (6) can be rearranged into the state-space representation of a linear time-invariant system with two inputs ([[delta].sub.f] and 6r) and two outputs ([beta] and [psi]).
In a time-invariant system, a time shift or delay of the input produces a corresponding shift in the output, without any other change.
Furthermore, the second-order ordinary differential equations for the dynamics can be transformed into first-order ordinary differential equations to form a linear, time-invariant system with no constraints, but the order of the system of equation increases.
Like [18, 19], the discrete linear time-invariant system in adversary disturbance which existed is expressed by

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