System Stability Using MATLAB Software 1

Stability is the most important system specification. If a system is unstable, transient response and steady-state errors are moot points. An unstable system cannot be designed for a specific transient response or steady-state error requirement. There are many definitions for stability, depending upon the kind of system or the point of view.

• A linear, time-invariant system is stable if the natural response approaches zero as time approaches infinity.
• A linear, time-invariant system is unstable if the natural response grows without bound as time approaches infinity.
• A linear, time-invariant system is marginally stable if the natural response neither decays nor grows but remains constant or oscillates as time approaches infinity.

Thus, the definition of stability implies that only the forced response remains as the natural response approaches zero. a stable system needed because in order to build certain system such as an aerofoil in aeroplane system a stable system play most important part in building in because the unstable system will make the whole part of the object that we will build is dangerous to human.