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Condition for the stability of linear time-invariant (LTI) control system

sufficient condition for Stability

All coefficients in the first column complete Routh array are the same sign

For a system with transfer function G^(s)=N(s)D(s)\hat{G}(s) = \frac{\mathcal{N}(s)}{\mathcal{D}(s)}

Input-output stability implies that all root of d(s)\mathcal{d}(s) are in the Left Half Plane (LHP)