Lyapunov function

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Lyapunov function

[lē′ap·ə‚nȯf ‚fəŋk·shən]
(mathematics)
A function of a vector and of time which is positive-definite and has a negative-definite derivative with respect to time for nonzero vectors, is identically zero for the zero vector, and approaches infinity as the norm of the vector approaches infinity; used in determining the stability of control systems. Also spelled Liapunov function.
References in periodicals archive ?
They derived a kinematic controller for two subsystem to obtain a desired velocity by Lyapunov functions.
Lyapunov functions have been the main tool used to obtain boundedness, stability and the existence of periodic solutions of differential equations, differential equations with functional delays and functional differential equations (see [2, 5, 26]).
The proof of stability of the control law is achieved by augmenting Lyapunov functions for the state tracking errors and parameter estimation errors.
We introduce gain coefficients in the Lyapunov functions for a set of synchronization transitory periods.
Summing the two time derivatives of the Lyapunov functions [V.
Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions," Multidimensional Systems and Signal Processing, 24(3): 395-415(2013).
Properties of the composite quadratic Lyapunov functions, IEEE Transactions on Automatic Control, 49, 1162-1167 (2004).
Their topics include advanced Lyapunov functions for Lur'e systems, the stabilization of persistently excited linear systems, the hybrid coordination of flow networks, exponential stability for hybrid systems with saturations, and reference mirroring for control with impacts.
Recently, Lyapunov functions are being applied within the fractional calculus to analyze the stability of dynamical systems.
It can be seen that processes CPIeq1, CPIeq2 and CPIeq3 have nonlinear gains that belong to the interval defined in the Equation (21), then as expected all processes have positive-definite Lyapunov functions and their derivatives are negative-definite characterizing asymptotic stability in the Lyapunov sense, conform presented in Figure 3(b).
In a comprehensive introduction to the qualitative theory of ordinary differential equations, Barreira and Valls (both mathematics, Instituto Superior Tecnico, Portugal) focus on the existence and uniqueness of solution, phase portraits, linear equations and their perturbations, stability and Lyapunov functions, hyperbolicity, and equations in the plane.
Haddad and Chellaboina present sufficient conditions for an absolute stability problem involving a dynamical system with memoryless, time-varying feedback nonlinearities, and construct Lyapunov functions for interconnected dynamical systems by appropriately combining storage functions for each subsystem.