Under some assumptions and conditions, a sufficient condition is given for the closed-loop system to be stable based on Lyapunov theory and invariable set theory.
In this optimal method the controller coefficients are obtained as the functions of a free parameter, where this parameter needs to be chosen by the designer such that it should be near to the maximum operating frequency of the system, besides on the other hand the closed-loop system to be stable.
It is shown that constraint admissibility of local robust controllers is sufficient for the global closed-loop system to be stable, and how these controllers are related to more complex forms of control such as tube-based distributed model predictive control implementations.
For an unstable LRP, our attention is focused on the design of an L2 L∞ static state feedback controller and an L2 L∞ dynamic output feedback controller, both of which guarantee the corresponding closed-loop LRPs to be stable along the pass and have a prescribed L2 L∞ performance.
The structures on the Si 001) surface composed of close ad-dimers are believed to be stable [6, 13] or at least metastable [43].
By Lyapunov method, the overall closed-loop system is shown to be stable.
By control Lyapunov method, the overall closed-loop system is shown to be stable.
By using fuzzy inference systems, a state observer and H∞ tracking technique, the decentralized combined indirect and direct adaptive fuzzy control algorithm is developed based upon a united H∞ tracking controller design for the modification of the previous work of Huang et al. The resultant closed-loop systems are guaranteed to be stable and a good H∞ tracking performance is obtained.
That is to say, if the competition affects the coefficients among the three populations a and b satisfying the condition (0< a+b<2), then the densities of the populations X, Y, and Z will eventually trend to be stable and close to the equilibrium point ((x^{mathrm{eq}}, y^{mathrm{eq}}, z^{mathrm{eq}})).
There is evidence in support of Selten's stability prediction in the sense that the data from a game predicted to be stable comes closer to Nash equilibrium than data from a game predicted to be unstable.
