Stability Analysis of Mathematical Model

As was mentioned in the complex integration, it is often necessary in control theory to know if a system is stable or not. It is unstable if terms exist in the solution for the output that either increase without limit or oscillate with ever increasing amplitude. Thus terms of the form et, t2, t sin (nt), in the solution would lead to an unstable system, but those of the form e-t, sin (nt), te-2t, cos (nt) would indicate a stable system. With this problem we are going to investigate same model for investigation of this phenomena, related to stable or otherwise.