Algorithm Stability Analysis Using MATLAB: Implementation and Practical Applications

This article discusses methodologies for performing algorithm stability analysis using MATLAB. We can further examine both advantages and limitations of this approach while demonstrating its practical implementation through code examples. For instance, MATLAB's built-in functions like eig() for eigenvalue computation and roots() for polynomial root finding can be utilized to analyze system stability through pole-zero plots and frequency response analysis. The implementation typically involves defining system transfer functions using tf() or state-space models with ss(), followed by stability criteria evaluation through Nyquist plots or Routh-Hurwitz analysis. Additionally, we explore alternative stability analysis techniques including Lyapunov methods and numerical simulation approaches to comparatively assess MATLAB's capabilities. Practical engineering applications include control system design where stability margins are calculated using margin() function, and signal processing algorithms where stability is verified through impulse response convergence tests. Through MATLAB scripts incorporating error handling with try-catch blocks and parameter sweeping loops, engineers can automate stability verification for varying operating conditions. This comprehensive discussion enables readers to understand fundamental stability analysis concepts while gaining practical skills for implementing these techniques in real-world engineering challenges.