Linear system

A system is linear when its response to a weighted sum of inputs equals the same weighted sum of the separate responses. This superposition property is central to analyzing such systems.

Superposition principle: A property stating that a linear system's response to a sum of inputs equals the sum of their responses. It is the defining test for linearity in system behavior.
Homogeneity (systems): The property that scaling an input scales a system's output by the same factor. Homogeneity is one half of the superposition requirement.
Linear control theory: The study of controlling systems modeled by linear equations. It uses linear system models to design feedback and predict stability.
Nonlinear system: A system whose input-output relation fails at least one condition of superposition. Its responses cannot generally be assembled by adding scaled individual responses.
Impulse response: A system's output when its input is a unit impulse. For a linear time-invariant system, this response determines outputs for arbitrary inputs.
Additivity (systems): The property that a system's response to summed inputs equals the sum of their separate responses. Additivity is the other half of the linearity test.
Digital signal processing: The analysis and manipulation of signals represented as discrete numerical sequences. Linear filters are core tools for shaping sampled signals.
Saturation (control theory): A nonlinear effect in which an output or actuator stops increasing beyond a limit. Saturation breaks proportional response even when the unsaturated model is linear.
Convolution: A mathematical operation combining two functions to describe how one spreads or filters the other. It computes outputs by combining an input with the system's impulse response.
Time-invariant system: A system whose behavior does not change when its input is shifted in time. Time invariance is often paired with linearity but is a separate property.

Linked from 29 pages