Abstract
A New Set of Stability Criteria Extending Lyapunov's Direct Method
Highlights
Consider a continuous time dynamical system x = f (x, t) (1)where x ∈ Rn is a point in an n-th dimensional space and t is a one dimensional variable representing time. x(t) is the state of the dynamical system at time t and represents the trajectory of the point Copyright © SIAMUnauthorized reproduction of this article is prohibited as time passes
Stability is an important topic in the studies of the dynamical system
Stability is an important topic in the studies of the dynamical systems
Summary
Where x ∈ Rn is a point in an n-th dimensional space and t is a one dimensional variable representing time. x(t) is the state of the dynamical system at time t and represents the trajectory of the point. X(t) is the state of the dynamical system at time t and represents the trajectory of the point. Rather than solving (1) analytically, the method employs a scalar positive definite function V (x, t) intuitively representing the energy of the state, where V (x∗, t) = 0 and V (x, t) > 0 for any x = x∗. If V (x, t) < 0 for any x except at x∗, the energy decreases monotonically over time and the trajectory converges to x∗.
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