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1. Definition

   • A system is stable if the roots of the characteristic equation are real Negative or complex conjugate with negative real part. Or said in form more compact, if all the roots are in the left half-plane of the complex variable s.

2. Asymptotic stability

   • A system is asymptotically stable if for all possible initial conditions its zero-entry response approaches zero over time.

3. Stability in impulse response

   • A system is said to be stable in the direction of the impulse response if its response to an impulse input approaches zero over time

4. Bounded Input Bounded Output

   • A BIBO system is stable if its output is limited for each limited entry

5. Marginally stable

   • A system is marginally stable when all its poles are in the left half-plane, except for one at the origin or by complexes conjugated with zero real part

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