If a given function V is radially unbounded, does it also imply that it is positive definite? I am trying to solve a stability problem (prove GAS) with and without Lasalle's theorem. It is easy enough to solve using Lasalle's theorem as I can prove the function is radially unbounded but do not know how to see if V (Lyapunov function) is positive definite.
2026-03-27 04:56:48.1774587408
Lyapunov stability and Lasalle's Theorem
163 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in NONLINEAR-SYSTEM
- Solving special (simple?) system of polynomial equations (only up to second degree)
- Determination of Invertibility
- Question about stability of a nonlinear dynamical system
- The equation $x^T A x = (x^2)^T A x^2$
- 1D viscous flow upwards against gravity
- Convergence of fixed-point in a gauss-seidel style
- Intuition behind dense orbits
- Determine the stability properties and convergence in the origin using Lyapunov Direct Method
- Is $x(t/2)$ a causal/memoryless system?
- Why this field with non-zero curl has closed orbit?
Related Questions in LYAPUNOV-FUNCTIONS
- Deriving inequality from a Lyapunov test of $x' = -x + y^3, \space y' = -y + ax^3$
- Question about stability of a nonlinear dynamical system
- Determine the stability properties and convergence in the origin using Lyapunov Direct Method
- When is $A^TR + RA = -2RA$
- Finding a unique fixed point for a dynamical system
- How to find a Lyapunov function?
- Special case of Lyapunov equation $AP+PA=-I$
- Lyapunov Function for Nonlinear Systems
- Finding a Lyapunov function for modified quadratic form
- Lyapunov function for predator-prey system
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?