Stability Analysis of Linear Control Systems by Wall’s Continued Fraction Expansion

Based on a particular continued fraction expansion, the Euclidean division scheme, and the Faddeev–LeVerrier algorithm, we propose an innovative approach to stability analysis for linear time-invariant control systems. Our method offers a comprehensive analytical framework that facilitates the determination of the range of stable controller gains for closed-loop systems, whether presented in the frequency domain or the state space. Unlike the Routh–Hurwitz criterion, our technique is exempt from the ad hoc rules that govern specific cases, thus advancing analytical rigor. Moreover, in certain scenarios, our method allows for the identification of instability midstream, thereby conserving computational resources. The proposed method is conceptually lucid and readily implementable, as exemplified by three illustrative instances.