Routh-Hurwitz Stability Criterion Animation

Shows dynamic Routh table construction, pole trajectories in complex plane, and impulse responses as system parameter varies.

Educational animation tool for understanding the Routh-Hurwitz stability criterion through dynamic visualization. This tool demonstrates how system stability changes as a parameter varies in the characteristic polynomial D(s) = s³ + 2s² + 3s + a₀.

The animation provides comprehensive multi-panel visualization: dynamic Routh table construction with color-coded sign indicators, Routh array bar chart highlighting positive/negative values, pole trajectories in the complex plane showing migration across the stability boundary, and corresponding impulse responses. The tool automatically identifies critical parameter values where stability transitions occur (a₀ = 6 in the example).

Features include step-by-step Routh table construction, sign change detection for stability analysis, stable/unstable region visualization in complex plane, pole movement tracking, and synchronized impulse response display. The animation makes abstract stability concepts concrete by showing the direct connection between Routh criterion results and pole locations.

Perfect for control engineering education, helping students visualize relationships between algebraic stability criteria (Routh-Hurwitz) and geometric pole placement. Generates high-quality MP4 animations and snapshots suitable for lectures and presentations. Users can easily modify the characteristic polynomial to explore different systems.

Compatible with MATLAB R2016b and later. Requires Control System Toolbox.