§33 The Stability Issue Typical solution- Lyapunoff Criteria If the state equation of a system is: dxn /dt= anmXm, nE(1, N then its eigen-equation is: AA-n=0 (1) If the real part of all roots of the eigen-equation are negative, then the undisturbed motion is always asymptotically stable. (2)If there exists at least one root with positive real part, then the undisturbed motion is always unstable (3)Direct Lyapunove Criterion(see references)§3.3 The Stability Issue Typical solution – Lyapunoff Criteria If the state equation of a system is: dx /dt = a x , n m (1,N) nm m=1 N n then its eigen-equation is: |A-|=0 (1) If the real part of all roots of the eigen-equation are negative, then the undisturbed motion is always asymptotically stable. (2) If there exists at least one root with positive real part, then the undisturbed motion is always unstable. (3) Direct Lyapunove Criterion (see references)