Math Problem Statement
A linearisation of a nonlinear state-space model about an equilibrium point has the following A matrix:
What can you say about the stability of this equilibrium point using Lyapunov’s First Method?
Group of answer choices
The EP is unstable.
The EP is marginally Stable.
Nothing can be said using this method.
The EP is Lyapunov Stable.
The EP is Asymptotically Stable.
Solution
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Math Problem Analysis
Mathematical Concepts
Nonlinear Systems
State-Space Models
Lyapunov's First Method
Stability Analysis
Eigenvalues
Formulas
Lyapunov's stability condition: Re(λ) < 0 for asymptotic stability
Eigenvalue analysis of A matrix
Theorems
Lyapunov's First Method
Stability criteria based on eigenvalues
Suitable Grade Level
Undergraduate Engineering or Mathematics