Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the n...
This paper presents a method for constructing polynomial Lyapunov functions to analyze the stability of nonlinear dynamical systems. The approach is based on genetic programming, a variant of genetic algorithms where the search space consists of hier...
In this paper, a rigorous Lyapunov direct method (LDM) is proposed to analyze the stability of fractional non-linear systems involving Hadamard or Caputo–Hadamard derivatives. Based on the characteristics of Hadamard-type calculus, several new...
The crack growth process in metals can be continuously monitored and recorded in real time using highly sensitive acoustic emission technology. To predict this complex behavior, an improved largest Lyapunov exponent method, enhanced by a small data o...
The purpose of this paper is to investigate some qualitative properties of solutions of nonlinear fractional retarded Volterra integro-differential equations (FrRIDEs) with Caputo fractional derivatives. These properties include uniform stability, as...
This paper deals with systematic approaches for the analysis of stability properties and controller design for nonlinear dynamical systems. Numerical methods based on sum-of-squares decomposition or algebraic methods based on quantifier elimination a...
The paper studies numerical methods that preserve a Lyapunov function of a dynamical system, i.e., numerical approximations whose energy decreases, just like in the original differential equation. With this aim, a discrete gradient method is implemen...
In this paper, applying some properties of matrix inequality and Schur complement, we give new upper and lower bounds of the solution for the unified algebraic Lyapunov equation that generalize the forms of discrete and continuous Lyapunov matrix equ...
The road friction coefficient is a key parameter for autonomous vehicles and vehicle dynamic control. With the development of autonomous vehicles, increasingly, more environmental perception sensors are being installed on vehicles, which means that m...
In this paper, we consider the numerical solution of large-scale discrete-time projected Lyapunov equations. We provide some reasonable extensions of the most frequently used low-rank iterative methods for linear matrix equations, such as the low-ran...
In this paper, a Lyapunov-based method is used in order to determine the stability boundaries of the grid-connected voltage source converter (VSC). To do so, a state space model of the VSC is used to form the Lyapunov function of the system. Then, by...
This article presents a Lyapunov precise integral-based analysis method for seismic structures with added viscous fluid dampers. This study uses the full stress algorithm as the optimization method, considering the mean square of interstory drifts as...
In this paper, we study the bisymmetric and skew bisymmetric solutions of quaternion generalized Lyapunov equation. With the help of semi-tensor product of matrices, some new conclusions on the expansion rules of row and column of matrix product on q...
This paper investigates the finite-time stability of a class of fractional-order switched systems with order 0<α<1, employing the fractional Lyapunov direct method. First, based on the Mittag-Leffler function and Gronwall inequality, two...
Controlling stability of dynamical systems is one of the most important challenges in science and engineering. Hence, there appears to be continuous need to study and develop numerical algorithms of control methods. One of the most frequently applied...
The aim of the paper was to analyze the given nonlinear problem by different methods of computation of the Lyapunov exponents (Wolf method, Rosenstein method, Kantz method, the method based on the modification of a neural network, and the synchroniza...
This paper investigates the tracking problem of fractional-order multi-agent systems. Both the order and parameters of the leader are unknown. Firstly, based on the positive system approach, the asymptotically stable criteria for incommensurate linea...
First, we set up in an appropriate way the initial value problem for nonlinear delay differential equations with a Riemann-Liouville (RL) fractional derivative. We define stability in time and generalize Mittag-Leffler stability for RL fractional dif...
Anomaly identification for internal combustion engine (ICE) sensors has become an important research area in recent years. In this work, a proposed indirect fuzzy Lyapunov-based computed ratio observer integrated with a support vector machine (SVM) w...
This article studies the generalized Mittag–Leffler stability of Hilfer fractional nonautonomous system by using the Lyapunov direct method. A new Hilfer type fractional comparison principle is also proved. The novelty of this article is the fr...
In this article, input-to-output stability (IOS) for stochastic complex networked control systems (SCNCS) is investigated. By applying Kirchhoff’s matrix tree theorem in graph theory, an appropriate Lyapunov function is established which is rel...
The present work is devoted to the study of nonlinear vibrations of an electromagnetically actuated cantilever beam subject to harmonic external excitation. The soft actuator that controls the vibratory motion of such components of a robotic structur...
In this paper, the non-scaling backstepping approach is used to examine the controller design process and stability analysis of a class of leader-type stochastic nonlinear systems. By utilizing the non-scaling backstepping design method and Lyapunov...
The article focuses on a design and experimental verification of continuous nonlinear systems control based on a new control structure based on a linear reference model. An application of Lyapunov’s second method ensures its asymptotic stability cond...
In this study, the problem of the stabilisation of a class of nonautonomous nonlinear systems was studied. First, a fractional stability theorem based on a fractional-order Lyapunov inequality was formulated. Then, a novel fractional-order sliding su...
We present two control strategies for an oscillating water column-wave energy converter (OWC-WEC) in the time domain. We consider a fixed OWC-WEC on the open sea with an impulse turbine module. This system mainly consists of a chamber, turbine and el...
This paper investigates the stabilization for stochastic coupled Kuramoto oscillators (SCKOs) via nonlinear distributed feedback control. An original nonlinear distributed feedback control with the advantages of fast response, no steady-state deviati...
This paper studies noise-to-state stability in probability (NSSP) for random complex dynamical systems on networks (RCDSN). On the basis of Kirchhoff’s matrix theorem in graph theory, an appropriate Lyapunov function which combines with every s...
This paper is intended to study noise-to-state stability in probability (NSSP) for random coupled Kuramoto oscillators with input control (RCKOIC). A feedback control is designed, which makes us give the existence and uniqueness of a solution for RCK...
The synchronization problem for impulsive fractional-order neural networks with both time-varying bounded and distributed delays is studied. We study the case when the neural networks and the fractional derivatives of all neurons depend significantly...
The general delay Hopfield neural network is studied. We consider the case of time-varying delay, continuously distributed delays, time-varying coefficients, and a special type of a Riemann–Liouville fractional derivative (GRLFD) with an expone...
Some inequalities for generalized proportional Riemann–Liouville fractional derivatives (RLGFDs) of convex functions are proven. As a special case, inequalities for the RLGFDs of the most-applicable Lyapunov functions such as the ones defined a...
In general, it is not easy work to design controllers and observers for high-order nonlinear systems. Planar motors that are applied to semiconductor wafer-stage processes have 14th-order nonlinear dynamics and require high resolution for position tr...
Quadrotors play a crucial role in the national economy. The control technology for quadrotor-slung load transportation systems has become a research hotspot. However, the underactuated load’s swing poses significant challenges to the stability...
The work focuses on the minimization of the body deflection from its equilibrium position after a deflection by force applied to the wheel with the task of simulating obstacles encountered by the wheel. The model presents a quarter of the car’s...
This article is devoted to a study of the question of existence (in time) of weak solutions and the derivation of qualitative properties of such solutions for the nonlinear viscoelastic wave equation with variable exponents and minor damping terms. B...
Floating offshore wind turbines (FOWTs) unlock superior wind resources and reduce operational barriers. The dynamics of FOWT platforms present added engineering challenges and opportunities. While the motion of the floating platform due to wind and w...
The present paper is devoted to the problems of practical stability with respect to h-manifolds for impulsive control differential equations with variable impulsive perturbations. We will consider these problems in light of the Lyapunov–Razumik...
To provide insights into the spreading speed and propagation dynamics of viruses within a host, in this paper, we investigate the traveling wave solutions and minimal wave speed for a degenerate viral infection dynamical model with a nonlocal dispers...
In this paper, we present a cancer system in a continuous state as well as some numerical results. We present discretization methods, e.g., the Euler method, the Taylor series expansion method, and the Runge–Kutta method, and apply them to the...
In this manuscript, we systematically investigate projective difference synchronization between identical generalized Lotka–Volterra biological models of integer order using active control and parameter identification methods. We employ Lyapuno...
In this paper, the problem of robust control of nonlinear fractional-order systems in the presence of uncertainties and external disturbance is investigated. Fuzzy logic systems are used for estimating the unknown nonlinear functions. Based on the fr...
The fractional differential equations involving different types of fractional derivatives are currently used in many fields of science and engineering. Therefore, the first purpose of this study is to investigate the qualitative properties including...
A well-known model of infectious diseases, described by a nonlinear system of delay differential equations, is investigated under the influence of stochastic perturbations. Using the general method of Lyapunov functional construction combined with th...
The stability of the nabla discrete distributed-order nonlinear dynamic systems is investigated in this paper. Firstly, a sufficient condition for the asymptotic stability of the nabla discrete distributed-order nonlinear systems is proposed based on...
The execution time that takes to perform numerical simulation of a chaotic oscillator mainly depends on the time-step h. This paper shows that the optimization of chaotic oscillators can be enhanced by estimating the highest h in either one-step or m...
In this paper, a numerical analysis of the oscillation equation with a derivative of a fractional variable Riemann–Liouville order in the dissipative term, which is responsible for viscous friction, is carried out. Using the theory of finite-di...
Stability studies remain a crucial aspect of power systems dynamic analysis, and are typically explored in three main categories: numerical methods, linearization techniques, or direct methods, which utilize Lyapunov energy functions. This paper belo...
We propose an iterative projection method for solving linear and nonlinear hypersingular integral equations with non-Riemann integrable functions on the right-hand sides. We investigate hypersingular integral equations with second order singularities...
This paper proposes a Distributed Adaptive Regularization Algorithm (DARN) for solving composite non-convex and non-smooth optimization problems in multi-agent systems. The algorithm employs a three-phase iterative framework to achieve efficient coll...
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