Stability of Linear Time-Invariant Systems

The stability of a single-input, single-output, singleloop, linear, time-invariant system is related to the properties of its open-loop gain. The impulse response of the open-loop system may be of the formg(t) = r + gₐ(t) + ∑ᵢ₌₀∞ gᵢ δ (t - tᵢ)whereris a nonnegative constant,gₐis integrable on[0, ∞), and∑ᵢ₌₀∞ |gᵢ|∞. If the Nyquist diagram of the open-loop gain does not go through nor encircle the critical point, then the closed-loop system is inputoutput stable, in the several meanings explained in the paper.