Estimation of the domain of attraction
Approaches used in estimating domain of attraction of equilibrium solution to system of nonlinear autonomous differential equation, and optimal selection of Liapunov function
LIAPUNOV FUNCTION↗
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Control of nonlinear multivariable systems
Control of nonlinear nonautonomous multivariable systems, based on Liapunov function
LIAPUNOV FUNCTION↗
LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL
Liapunov functions - automatic control
MATHEMATICS /GEN/↗
Study on determining stability domains for nonlinear dynamical systems Quarterly progress report no. 1, 1 May - 1 Aug. 1966
Numerical algorithm for determining stability domain of attraction of equilibrium motions of nonlinear dynamical systems - Liapunov functions
DYNAMIC STABILITY↗
Lyapunov functions for a class of n-th order nonlinear differential equations.
Liapunov function from quadratic polynomial for n-order nonlinear differential equations
LIAPUNOV FUNCTION↗
Stability-boundary approximations for relay- control systems via a steepest-ascent construction of lyapunov functions.
Stability boundary approximations for relay- control systems via steepest-ascent construction of Liapunov functions
STEEPEST ASCENT METHOD↗
Lyapunov functions and the exact differential equation
Liapunov functions and exact differential equation
Chen, C.-S.↗
Lyapunov functions for a class of Nth order nonlinear differential equations
Sequential development of quadratic polynomial into Liapunov function for nonlinear differential equations
SEQUENTIAL ANALYSIS↗
Liapunov criteria for weak stochastic stability.
Sufficient conditions for recurrence and positivity of diffusion process defined by stochastic differential equation, using Liapunov function
DIFFERENTIAL EQUATION↗
Fundamental Concepts of Stability Theory
Theorems and definitions for generation of Liapunov functions for analysis of linear and nonlinear dynamic systems
LIAPUNOV FUNCTION↗
Asymptotic stability of sampled nonlinear systems with variable sampling periods -- A bionic application Discussion
Developing Vidals and Laurents criteria for asymptotic stability of nonlinear sampled system using Liapunov functions
NONLINEAR SYSTEM↗
A matrix for evaluating Schwarz's form.
Transformation matrix converting phase variable form into Schwartz form for application to Liapunov function and Hurwitz criterion
SCHWARTZ METHOD↗
Stability of large-scale systems with stable and unstable subsystems.
The purpose of this paper is to develop new methods for constructing vector Liapunov functions and broaden the application of Liapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. With minor technical adjustments, the same criterion can be used to determine connective asymptotic stability of large-scale systems subject to structural perturbations. By redefining the constraints imposed on the interconnections among the subsystems, the considered class of systems is broadened in an essential way to include composite systems with unstable subsystems. In this way, the theory is brought substantially closer to reality since stability of all subsystems is no longer a necessary assumption in establishing stability of the overall composite system.
Grujic, Lj. T.↗
Research and study in system optimization techniques progress report, 14 nov. 1964 - 14 feb. 1965
System optimization techniques - motion stability study on Liapunov function application to finding estimators and connection with differential equations
OPTIMIZATION↗
Application of Lyapunov stability theory to some nonlinear problems in hydrodynamics
Liapunov function for analyzing stability of nonlinear equilibrium solutions in hydrodynamics
LIAPUNOV FUNCTION↗
Finite time stochastic stability and the analysis of tracking systems.
Liapunov functions for finite time stochastic stability and analysis of tracking system
SYSTEM STABILITY↗
A generalized Zubov formulation for limit cycles in third order nonlinear systems.
Generalized Zubov formulation from Liapunov function of limit cycle behavior in third order nonlinear systems
TRAJECTORY ANALYSIS↗
Liapunov's second method
Stability theorem based on Liapunov function, and using invariance property of limit sets of solutions to differential equations
THEOREM PROVING↗