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Security Monitoring Using Converse Lyapunov Function
This chapter introduces a novel framework to construct the region of attraction (ROA) of a power system centered around a stable equilibrium by using...
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An accelerated lyapunov function for Polyak’s Heavy-ball on convex quadratics
In 1964, Polyak showed that the Heavy-ball method, the simplest momentum technique, accelerates convergence of strongly-convex problems in the...
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Smoothed Piecewise Linear Lyapunov Function for the First Order Dynamical Systems
The paper deals with the mathematical backgrounds of design piecewise single-variable Lyapunov functions. These backgrounds are based on the study of...
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Enhancing Stability in Autonomous Control Systems Through Fuzzy Gain Scheduling (FGS) and Lyapunov Function Analysis
Traditional control methods may struggle to adapt to the nonlinear and uncertain characteristics in Autonomous Vehicle Control. In recent years,...
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Stabilization via Polynomial Lyapunov Function
In this paper we summarize some recent results on local state feedback stabilization of a nonlinear system via a center manifold approach. A...
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Barrier Lyapunov Function-Based Finite-Time Dynamic Surface Control for Output-Constrained Nonstrict-Feedback Systems
This paper investigates a finite-time tracking problem for the uncertainty nonlinear systems in nonstrict-feedback form, in which the output signal...
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Asymmetric time-varying integral barrier Lyapunov function based adaptive optimal control for nonlinear systems with dynamic state constraints
This paper investigates the issue of adaptive optimal tracking control for nonlinear systems with dynamic state constraints. An asymmetric...
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Finite-Time Attitude Maneuver Control for Liquid-Filled Spacecraft with Attitude and Angular Velocity Constraints Based on Barrier Lyapunov Function
The attitude maneuver control problem for a liquid-filled spacecraft system is investigated in the presence of attitude and angular velocity...
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Performance and Stability Analysis of Enhanced Lyapunov Function and Predictive Voltage Control with Active Dam** for Single-Phase PV/Grid Electric Power System
As the world increasingly turns to renewable energy sources, the integration of solar photovoltaic (PV) systems into the grid has emerged as a...
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On the Preservation of a Quadratic Lyapunov Function of a Linear Differential Autonomous System under Constant Perturbations of the Coefficients
AbstractFor an autonomous linear homogeneous asymptotically stable differential system, we obtain sufficient conditions for the smallness of...
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A Discrete Analogue of the Lyapunov Function for Hyperbolic Systems
We study the difference splitting scheme for the numerical calculation of stable solutions of a two-dimensional linear hyperbolic system with...
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General Dynamical Systems with a Lyapunov Function
In this chapter we develop a turnpike theory for a class of general dynamical systems in a metric space with a Lyapunov function. This class of...
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On Determining the Coefficients of a Quadratic Lyapunov Function with Given Properties in the Case of Multiple Roots of the Characteristic Equation
AbstractFor continuous and discrete linear autonomous systems, we discuss the possibility of choosing the coefficients of the quadratic Lyapunov...
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The Rionero’s special type of Lyapunov function and its application to a diffusive epidemic model with information
We consider a SIR-like reaction-diffusion epidemic model which embeds opinion-driven human behavioural changes. We assume that the contagion rate is...
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Prescribed Performance-tangent Barrier Lyapunov Function for Adaptive Neural Backstep** Control of Variable Stiffness Actuator with Input and Output Constraints
Due to the complexity of modeling and the strong transmission coupling, the rich background of rigid actuator control has not been transferred to...
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Modular multi-phase DC–DC converter with enhanced dynamic performance based on Lyapunov function
DC–DC converters are among the main components of DC power systems based on renewable energy sources. In some applications, interleaved multi-phase...
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Barrier Lyapunov function-based adaptive fuzzy control for general dynamic modeling of affine and non-affine systems
In this paper, first, general dynamic modeling is proposed for multi-input/output nonlinear systems in the form of affine and non-affine systems....
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Lyapunov Function in the Hyper-Complex Phase Space
The paper deals with the development of background for defining Lyapunov functions for a wide range of linear dynamical objects. This background is...
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Estimation of Regions of Attraction of Dynamical Systems via Polynomial Lyapunov Function
While studying the behavior of a dynamical system, the problem of the stability of a stationary regime plays an important role. This task includes...
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Automated tight Lyapunov analysis for first-order methods
We present a methodology for establishing the existence of quadratic Lyapunov inequalities for a wide range of first-order methods used to solve...
