general rules of stability in control system

 1. a system is stable if its output is bounded for any bounded input.

 2. a system is asymptotically stable if, in the absence of output, the output tends toward zero irrespective of initial conditions. 

  3. a system is unstable if its output is unbounded for any bounded input. 

  4. stability of the system depends upon the poles.

  5. if all the poles are located in the left of the s-plane, then the system is stable.

  6. as pole approach to origin then stability decrease.