In control theory, the "'minimum energy control "'is the control u ( t ) that will bring a linear time invariant system to a desired state with a minimum expenditure of energy.
22.
In the study of dynamical systems, the "'method of averaging "'is used to study certain time-varying systems by analyzing easier, time-invariant systems obtained by averaging the original system.
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Although arbitrary wave shapes will propagate unchanged in lossless linear time-invariant systems, in the presence of dispersion the sine wave is the unique shape that will propagate unchanged but for phase and amplitude, making it easy to analyze.
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The QFT design methodology was originally developed for " Single-Input Single-Output " ( SISO ) and " Linear Time Invariant Systems " ( LTI ), with the design process being as described above.
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Keeping our aim at linear, time invariant systems, we can also characterize the multipath phenomenon by the channel transfer function H ( f ), which is defined as the continuous time Fourier transform of the impulse response h ( t)
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In accordance with the methods of linear time-invariant systems, by putting two different inputs into the integrator circuit, i _ 1 ( t ) \, and i _ 2 ( t ) \,, the two different outputs
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In the case of linear invariant systems, this is known as positive real transfer functions, and a fundamental tool is the so-called Kalman Yakubovich Popov lemma which relates the state space and the frequency domain properties of positive real systems.
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In control theory and in particular when studying the properties of a linear time-invariant system in state space form, the "'Hautus lemma "', named after Malo Hautus, can prove to be a powerful tool.
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If a time-invariant system is also linear, it is the subject of LTI system theory ( linear time-invariant ) with direct applications in NMR spectroscopy, seismology, Discrete time-invariant systems are known as shift-invariant systems.
30.
If a time-invariant system is also linear, it is the subject of LTI system theory ( linear time-invariant ) with direct applications in NMR spectroscopy, seismology, Discrete time-invariant systems are known as shift-invariant systems.