coefficients ai (t) and bk(t) depend only upon the independent variable t (e.g., time).
Initially relaxed linear systems possess the following property: Zero input yields zero output. An incrementally linear system is one that responds linearly to changes in the input; that is, the difference in the response to any two inputs is a linear function of the difference between the two inputs. Many of the characteristics of such systems can be analyzed using the techniques developed for linear systems. In reality, no physical system can be described exactly by a linear differential or difference equation. Many systems, however, can be represented over a limited operating range, or approximated by such equations.