Lyapunov functions/functionals have found their footing in Volterra integro-differential equations. This is not the case for integral equations, and it is therefore further explored in this paper. In this manuscript, we utilize Lyapunov functionals c...
State observers for systems having Lipschitz nonlinearities are considered for what concerns the stability of the estimation error by means of a decomposition of the dynamics of the error into the cascade of two systems. First, conditions are establi...
One of the main properties of solutions of nonlinear Caputo fractional neural networks is stability and often the direct Lyapunov method is used to study stability properties (usually these Lyapunov functions do not depend on the time variable). In c...
One approach to study various stability properties of solutions of nonlinear Caputo fractional differential equations is based on using Lyapunov like functions. A basic question which arises is the definition of the derivative of the Lyapunov like fu...
The traditional method of constructing a Lyapunov functional for dynamical systems with time delay is usually dependent on positive definite matrices in the quadratic form. In this paper, a new Lyapunov functional is proposed and the corresponding pr...
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...
Lyapunov functions enable analyzing the stability of dynamic systems described by ordinary differential equations without finding the solution of such equations. For nonlinear systems, devising a Lyapunov function is not an easy task to solve in gene...
This paper is concerned with the stability and stabilization problem of a Takagi-Sugeno fuzzy (TSF) system. Using a non-quadratic function (well-known integral Lyapunov fuzzy candidate (ILF)) and some lemmas, new sufficient conditions are established...
In recent years, various qualitative investigations of the properties of differential equations with different types of generalizations of Riemann–Liouville fractional derivatives were studied and stability properties were investigated, usually...
This paper develops a totally new appointed-time integral barrier Lyapunov function-based trajectory tracking algorithm for a hovercraft in the presence of multiple performance constraints and model uncertainties. Firstly, an appointed-time performan...
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, we study the structure of trajectories of discrete disperse dynamical systems with a Lyapunov function which are generated by set-valued mappings. We establish a weak version of the turnpike property which holds for all trajectories of...
This paper investigates the automatic berthing problem of underactuated surface vessels in the case of uncertain dynamics and yaw rate limitation, given the importance of yaw rate control and the unmeasurable hydrodynamic parameters of the vessel at...
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...
This paper addresses the problem of sampled-data control in T-S fuzzy systems with time delays. Initially, a negative-definite criterion is developed for the matrix containing membership functions with the help of the idea of a switching mechanism. B...
This paper presents an adaptive constraint control approach for Electronic Throttle Control System (ETCS) with asymmetric throttle angle constraints. The adaptive constraint control method, which is based on barrier Lyapunov function (BLF), is design...
In this paper, nonlinear nonautonomous equations with the generalized proportional Caputo fractional derivative (GPFD) are considered. Some stability properties are studied by the help of the Lyapunov functions and their GPFDs. A scalar nonlinear fra...
A fractional model of the Hopfield neural network is considered in the case of the application of the generalized proportional Caputo fractional derivative. The stability analysis of this model is used to show the reliability of the processed informa...
In this work, a new robust controller is designed for a second-order plant model, considering asymmetric output constraints. The tracking error convergence and output constraint are achieved by using a control law whose output feedback term is user-d...
This paper presents a novel control design methodology for a magnetorheological (MR) damper-based semi-active suspension system operating under communication-induced time delays, which introduce nonlinear sampled-data dynamics. To address these chall...
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...
Trajectory tracking control of input-constrained systems is an essential problem in many control applications, including robotics. In this paper, we propose a constrained tracking controller for input affine nonlinear systems with convex input constr...
This paper refers to fast and accurate electric servo control in the presence of position and velocity constraints. This problem, one of the most common nowadays in industrial automation, is often addressed by controllers derived using barrier Lyapun...
As with probability theory, uncertainty theory has been developed, in recent years, to portray indeterminacy phenomena in various application scenarios. We are concerned, in this paper, with the convergence property of state trajectories to equilibri...
In this paper, the structural properties of chemical reaction systems obeying the mass action law are investigated and related to the physical and chemical properties of the system. An entropy-based Lyapunov function candidate serves as a tool for pr...
This paper deals with the stabilization problem of a nonlinear system described by a Takagi–Sugeno fuzzy (TSF) model with unmeasurable premise variables via a robust controller. Applying the sector nonlinearity techniques, the nonlinear system...
The robust stabilization of the attitude of quadrotors with respect to disturbance torques is a fundamental and crucial control problem in many unmanned aerial vehicle (UAV) applications. For this problem, a control Lyapunov function (CLF)-based robu...
In this paper a system of nonlinear Riemann–Liouville fractional differential equations with non-instantaneous impulses is studied. We consider a Riemann–Liouville fractional derivative with a changeable lower limit at each stop point of...
Considering some unmeasurable states, a fuzzy static output control problem of nonlinear stochastic systems is discussed in this paper. Based on a modelling approach, a Takagi–Sugeno (T–S) fuzzy system, constructed by a family of stochastic different...
This paper further develops a relaxed method to reduce conservatism in
Collision avoidance and path planning are critical topics in autonomous vehicle development. This paper presents the progressive development of an optimization-based controller for autonomous vehicles using the Control Lyapunov Function–Control...
In this work, substrate control of a biological process with unknown varying control gain, input saturation, and uncertain reaction rate is addressed. A novel adaptive controller is proposed, which tackles the combined effect of input saturation and...
Flexible manipulators are widely applied in many fields. Here, the control design for a simplified flexible manipulator model with nonlinear inputs and state constraints is studied. The impact of two inputs and disturbances on the system was consider...
Renewable energy sources play a pivotal role in the pursuit of sustainable and eco-friendly power solutions. While offering environmental benefits, they present inherent challenges. Photovoltaic systems rely on surrounding conditions, wind systems co...
The modular multilevel converter–bidirectional DC–DC converter (MMC–BDC) has been proposed to be utilized in the vessel integrated power system to interconnect the medium voltage bus and the distributed energy storage elements. In the shipboard appli...
This work investigates the stability conditions for linear systems with time-varying delays via an augmented Lyapunov–Krasovskii functional (LKF). Two types of augmented LKFs with cross terms in integrals are suggested to improve the stability...
This study explores positioning and obstacle avoidance control for autonomous surface vehicles (ASVs) by considering equivalent elliptical-shaped obstacles. Firstly, compared to most Barrier Lyapunov function (BLF) methods that approximate obstacles...
Path planning and collision avoidance are essential components of an autonomous driving system (ADS), ensuring safe navigation in complex environments shared with other road users. High-quality planning and reliable obstacle avoidance strategies are...
This article aims to study parallelizable random dynamical systems by examining them through the terms of dissipation and stochastic Lyapunov functions. It is demonstrated that any random variable that is not a random fixed point admits a tube, and e...
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...
The global stability analysis for the mathematical model of an infectious disease is discussed here. The endemic equilibrium is shown to be globally stable by using a modification of the Volterra–Lyapunov matrix method. The basis of the method...
A model of gene regulatory networks with generalized Caputo fractional derivatives with respect to another function is set up in this paper. The main characteristic of the model is the presence of a switching rule, which changes at certain times at b...
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 paper proposes an output feedback controller with a linear extended state observer (LESO) for an n-degree-of-freedom (n-DOF) manipulator under the presence of external disturbance, an input dead-zone, and time-varying output constraints. First,...
In this work, we obtain a weak version of the turnpike property of trajectories of perturbed discrete disperse dynamical systems, which have a prototype in mathematical economics.
Generally, the continuous and discrete TS fuzzy systems’ control is studied independently. Unlike the discrete systems, stability results for the continuous systems suffer from conservatism because it is still quite difficult to apply non-quadr...
Convergence of a stochastic process is an intrinsic property quite relevant for its successful practical for example for the function optimization problem. Lyapunov functions are widely used as tools to prove convergence of optimization procedures. H...
Irreversibility (that is, the “one-sidedness” of time) of a physical process can be characterized by using Lyapunov functions in the modern theory of stability. In this theoretical framework, entropy and its production rate have been generally regard...
Recently, A.N. Gorban presented a rich family of universal Lyapunov functions for any linear or non-linear reaction network with detailed or complex balance. Two main elements of the construction algorithm are partial equilibria of reactions and conv...
The paper proposes three alternative extensions to the classical global-best particle swarm optimization dynamics, and compares their relative performance with the standard particle swarm algorithm. The first extension, which readily follows from the...
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