14.7 : 连续和离散时间系统的 BIBO 稳定性

The stability of systems can be ascertained using convolution.

If an input signal has a constant that ensures that the signal's modulus never exceeds it at any point in time, it is considered bounded.

A system is bounded-input bounded-output, also known as BIBO stable if any given bounded input signal invariably produces a bounded output. The figure illustrates examples of BIBO-stable and non-BIBO-stable systems.

The convolution integral can be used to assess BIBO stability when a bounded continuous-time input is applied to a Linear Time-Invariant system.

The boundedness of the input signal may be represented through a constant, and the convolution integral formulations determine the bounded output.

If the integrand is finite, the output is finite, meaning a continuous-time system with an absolutely integrable impulse response is BIBO stable.

This same process applies to discrete-time systems; a bounded output is achieved through the convolution integral.

The output is finite if the summation term has a finite value, indicating that a discrete-time system is BIBO stable if its impulse response is absolutely summable.