Stability Analyzer
Stability Analysis Results
How It Works
Analyze system stability in six simple steps:
Step 1: Input System
Enter characteristic polynomial or system matrix. Define system parameters.
Step 2: Choose Method
Select analysis method. Pick eigenvalue or Routh-Hurwitz approach.
Step 3: Calculate Eigenvalues
Find polynomial roots. Determine characteristic equation solutions.
Step 4: Check Stability Conditions
Verify eigenvalue locations. Apply stability criteria.
Step 5: Analyze Results
Interpret eigenvalue positions. Determine stability status.
Step 6: Display Conclusion
Show stability assessment. Provide complete analysis report.
Understanding System Stability
Learn about stability analysis and its applications:
System Stability
System behavior over time. Determines if output remains bounded.
Eigenvalues
Characteristic values of system matrix. Determine stability directly.
Characteristic Polynomial
Polynomial det(sI - A). Roots determine system eigenvalues.
Routh-Hurwitz Criterion
Test for polynomial stability. Counts sign changes in array.
BIBO Stability
Bounded input bounded output. Practical stability definition.
Lyapunov Stability
Equilibrium point stability. Energy-based analysis method.
Left Half Plane
Continuous system stability region. Eigenvalues must be here.
Unit Circle
Discrete system stability region. Eigenvalues inside circle.
Marginal Stability
Eigenvalues on imaginary axis. Boundary between stable unstable.
Asymptotic Stability
System converges to equilibrium. Strongest stability form.
Control System Design
Ensure system stability through controller design. Engineering application.
Pole Placement
Move eigenvalues to desired locations. Feedback control method.
Key Features
Explore powerful stability analysis capabilities:
Multiple Analysis Methods
Eigenvalue, Routh-Hurwitz, and Lyapunov methods. Comprehensive approach.
System Type Support
Linear, nonlinear, and discrete systems. Versatile analysis capability.
Eigenvalue Calculation
Compute all system eigenvalues automatically. Complete pole analysis.
Routh Table Generation
Build Routh-Hurwitz stability table. Visual stability assessment.
Detailed Analysis Report
Comprehensive stability assessment with explanations. Learn system behavior.
100% Private & Secure
All calculations happen locally in browser without sending data to servers. Complete privacy guaranteed with no data collection.
Related Tools
Explore complementary mathematical analysis tools:
Frequently Asked Questions
Find answers to common questions about stability analysis:
What is system stability?
System behavior remains bounded over time. Learn more at Khan Academy.
How do eigenvalues determine stability?
Eigenvalues in left half-plane = stable. Check Wolfram MathWorld.
What is Routh-Hurwitz criterion?
Test for polynomial stability without finding roots. Practical assessment method.
When is system marginally stable?
Eigenvalues on imaginary axis. See Britannica.
Is my data stored?
No, all calculations happen locally in your browser. Data is never sent to servers or stored. Your privacy is completely protected.