According to Lyapunov stability theory, systems (7) when (h(t)=0) are asymptotically stable.
Analytical and numerical methods for solution, as well as controllability and stability theory for systems of DDEs, are nearly as rich and developed as those for ordinary differential equations.
By using Lyapunov stability theory, the overall system with the proposed controller has been proved to be uniform ultimate bounded.
end{aligned} (21) The rest of the proof is similar to Theorem 3.1 According to the Lyapunov stability theory, the error system is asymptotically stable.
Similar to the above analysis in Theorem 3.1, we can get (alpha ^{T} k)hat{Omega}alpha k)<0), and it follows from Lyapunov stability theory that the system (34) is globally asymptotically stable.
It is then shown that the observer and the controlled system form a cascaded structure, which allows the application of the finite-time stability theory of cascaded systems to prove the finite-time stability of the closed-loop system.
Based on the bifurcation and stability theory of dynamical systems, the symmetric/asymmetric bifurcation behaviours and chaotic motions of a railway bogie system under a complex nonlinear wheel rail contact relation are investigated in detail by the 'resultant bifurcation diagram' method with slowly increasing and decreasing speed.
By using properties of the Laplacian matrix and combining the stability theory of impulsive systems, necessary and sufficient conditions are derived to achieve the formation tracking of the second-order multi-agent system with and without the input delay, respectively.
It gives a universal tool that makes it possible to come close to solving fundamental problems in general stability theory for singular systems dynamics, including decomposition problem.
Based on the stability theory of fractional systems and the inequality of the fractional derivative, some pinning synchronization criteria are abtained for both directed and undirected complex networks.
