It is necessary just to test if it satisfies superposition and homogeneity properties.
If this is a classic black box Input-(Unknown Transformation) - Output, well, you vary inputs and look if outputs change linearly or non-linearly.
To get a more illuminating answer you should be somewhat more specific.
@Alexey Kartashov. yaa. that is true. but now problem is how many time and what should be the range of frequency should i cover so that it can ensure me system is linear or nonlinear.
because recently i have solved a problem in matlab. here i have taken nonlinear system as my system and i try to verify by changing input. believe me it is showing system is linear for some frequency range and nonlinear for some frequency. so i am confused about how to ensure that system is correctly tested??
The control parameters of a system (λ) drive the system in linear or non-linear phase. In a set of λ the system go in linear phase and in an other set of λ go to non-linear phase. Many systems have this feature. Try to compute the spectrum of the Lyapunov exponents.
You can also excite it with a sinusoidal input and take the spectrum of the answer. Nonlinear systems usually respond with the frequency of excitation and sub or super harmonics. If the system is linear, this will not happen.
You just have to be careful about waiting for long enough for the transient response to vanish.
I think it's not enough to test the superposition because it must be achieved whatever the input is. For example "Operational Amplifier" has saturation for some inputs according to its gain.
Very stimulating question!
I would visualize it in order to see whether it is nonlinear or not, e.g., urban growth and evolution of social media.
Jiang B. (2015), Head/tail breaks for visualization of city structure and dynamics, Cities, 43, 69-77, Preprint: http://arxiv.org/abs/1501.03046
Jiang B. and Miao Y. (2014), The evolution of natural cities from the perspective of location-based social media, The Professional Geographer, xx(xx), xx-xx, DOI: 10.1080/00330124.2014.968886, Preprint: http://arxiv.org/abs/1401.6756
- Badges
- Science topic
- Similar topics
- Engineering
- Control Theory
- Control Systems
- Control Systems Engineering