BOUNDEDNESS AND UNIFORM BOUNDEDNESS RESULTS FOR CERTAIN NON-AUTONOMOUS DIFFERENTIAL EQUATIONS OF FOURTH ORDER

Sufficient conditions have been obtained so that all solutions of a different fourth order differential equation are bounded and uniformly bounded.

Stability and Uniform Boundedness for a Class of Anaerobic Digestion Ecological Models

Stability, boundedness and persistence are three important aspects for an ecological model. In this paper, a further analysis of a class of anaerobic digestion ecological models is performed. Based on the Liupunov Method, the local stability of all equilibria in the system is got. According to the vector fields described by the system, the proof of the boundedness of the solution on the anaerobic digestion processes is completed in three steps. The method proposed in the discussion on the boundedness can be generalized to the similar problems. Results in this paper give information on how to run the ecological system well by adjusting the system parameters.

Uniformly ultimate boundedness for discontinuous systems with time-delay

The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed.Based on the Lyapunov-Krasovskii functional,the Lyapunov theorem for the globally strongly uniformly ultimate boundedness of retarded discontinuous systems is presented.Furthermore,the result is applied to a class of mechanical systems with a retarded discontinuous friction item.

Robust adaptive control for interval time-delay systems

This paper focuses on the robust adaptive control problems for a class of interval time-delay systems and a class of large-scale interconnected systems. The nonlinear uncertainties of the systems under study are bounded by high- order polynomial functions with unknown gains. Firstly, the adaptive feedback controller which can guarantee the stability of the closed-loop system in the sense of uniform ultimate boundedness is proposed. Then the proposed adaptive idea is extended to robust stabilizing designing method for a class of large-scale interconnected systems. Here, another problem we address is to design a decentralized feedback adaptive controller such that the closed-loop system is stable in the sense of uniform ultimate boundedness for all admissible uncertainties and time-delay. Finally, an illustrative example is given to show the validity of the proposed approach.

An Improved Robust Adaptive Control Design for a Class of Neutral Delay Systems

The problem of adaptive robust control is addressed for a class of neutral delay systems. All uncertainties are assumed to be bounded by unknown constants. An improved adaptation law is proposed to estimate the square of these unknown bounds. Then, by making use of the updated values of the squared unknown bounds, an adaptive controller is designed to make the solution of the resultant closed-loop system uniformly ultimately bounded. Furthermore, this method avoids chattering and improves the performance. An example is given to illustrate the effectiveness of this method.

A New Uniformly Ultimate Boundedness Criterion for Discrete-Time Nonlinear Systems

A new type criterion of globally uniformly ultimate boundedness for discrete-time nonlinear systems is introduced. In classical Lyapunov theory about globally uniformly ultimate boundedness, Lyapunov function is assumed to be positive definite and its difference at the every latter moment and the former moment is negative definite. In this paper the condition of difference of Lyapunov function is relaxed. Under the relaxed condition, the result of this paper can be considered as the extension of the classical Lyapunov theory about uniformly ultimate boundedness.

Uniform Boundedness for Neutral Equations with Unbouned Delay

We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.

THE UNIFORM BOUNDEDNESS PRINCIPLE IN SOME TOPOLOGICAL VECTOR GROUPS

It is shown that the famous Banach-Steinhaus theorem can be generalized to some families of nonlinear functionals defined on some topological groups and topological vector space, e.g. the F-spaced lβ(0 <β < 1) and S[a, b].

Tracking Control of Uncertain Nonlinear Systems With Unknown Constant Input Delay

A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.

A Remark on the Uniform Convergence of Some Sequences of Functions

We stress a basic criterion that shows in a simple way how a sequence of real-valued functions can converge uniformly when it is more or less evident that the sequence converges uniformly away from a finite number of points of the closure of its domain. For functions of a real variable, unlike in most classical textbooks our criterion avoids the search of extrema (by differential calculus) of their general term.

The Existence of Solutions of a Space-Uniform Boltzmann Equation

Boltzmann equation is an equation which is related to the three variables of x, v, t. In this paper, we mainly study the space-uniform Boltzmann equation which unknown function F is not related to the position variable x. We mainly use the contraction mapping theorem to find the existence of the solution, so our mainly work is to prove the self-mapping, i.e. to prove its uniformly bounded, and then to prove the contraction mapping. There we can get the range of ||B(θ)||L1(L∞), next we can figure out the range of M and T from the conditions what we know. Finally, from these conditions, we can find the existence of the solution.

Uniformly Bounded Set-Valued Composition Operators in the Spaces of Functions of Bounded Variation in the Sense of Riesz

We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function.

Uniform boundedness of the solutions of functional differential equations with infinite delay

This note deals with the functional differential equations with infinite delay x’=f（t, x,）, （1）where x∈Rn, f: [0,∞) ×C9→Rn, Cg is the phase space of （1）, which is defined as follows:C=∮(（-∞, 0], Rn） is the set of all the continuous vector-functions mapping (-∞, 0] toRn. The function g:（-∞, 0]→ [1, ∞） is continuous and nonincreasing with g （0）=1 andg（-∞）=∞.

UNIFORM BOUNDEDNESS AND STABILITY OF SOLUTIONS TO A CUBIC PREDATOR-PREY SYSTEM WITH CROSS-DIFFUSION

Using the energy estimate and Gagliardo-Nirenberg-type inequalities,the existence and uniform boundedness of the global solutions to a strongly coupled reaction-diffusion system are proved. This system is a generalization of the two-species Lotka-Volterra predator-prey model with self and cross-diffusion. Suffcient condition for the global asymptotic stability of the positive equilibrium point of the model is given by constructing Lyapunov function.

UNIFORM BOUNDEDNESS AND UNIFORM STABILITY OF A KIND OF DELAY──DIFFERENTIAL EQUATIONS

This paper presents a discussion of differential equations with two terms generated by delays. They are as follows x′(t) = a(t)x(t - p(t)) - b(t)x(t - r(t)).Sufficient conditions for its solution with uniform bound and for its zero solution with uniform stability are established.

UNIFORM ULTIMATE BOUNDEDNESS AND PERIODIC SOLUTIONS TO NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS

In this paper, the existence of periodic solution to nonlinear integro-differential equations with infinite delay is studied in the phase space (Cg,|·|g). We prove that the g-uniformly ultimately bounded solutions implies the existence of periodic solutions using Horn’s fixed point theorem. Some known results are generalized, including the famous Yoshizawa’s theorem.

滞后型脉冲泛函微分方程有界性的Lyapunov逆定理

本文通过建立滞后型脉冲泛函微分方程饱和解的存在唯一性定理,在广义常微分方程与滞后型脉冲泛函微分方程等价的基础上,研究了滞后型脉冲泛函微分方程关于一致有界性的Lyapunov逆定理.

具有Leslie-Gower项的捕食者-食饵扩散模型的稳定性

讨论具有Leslie-Gower项的捕食者-食饵弱耦合扩散系统解的一致有界性和正平衡点的稳定性。首先,应用线性化方法得出了该模型正平衡点的局部稳定性的充分条件。其次,应用Lyapunov函数方法得出了该模型正平衡点的全局渐近稳定性的充分条件。

A New Robust Adaptive Neural Network Backstepping Control for Single Machine Infinite Power System With TCSC

For a single machine infinite power system with thyristor controlled series compensation(TCSC) device, which is affected by system model uncertainties, nonlinear time-delays and external unknown disturbances, we present a robust adaptive backstepping control scheme based on the radial basis function neural network(RBFNN). The RBFNN is introduced to approximate the complex nonlinear function involving uncertainties and external unknown disturbances, and meanwhile a new robust term is constructed to further estimate the system residual error,which removes the requirement of knowing the upper bound of the disturbances and uncertainty terms. The stability analysis of the power system is presented based on the Lyapunov function,which can guarantee the uniform ultimate boundedness(UUB) of all parameters and states of the whole closed-loop system. A comparison is made between the RBFNN-based robust adaptive control and the general backstepping control in the simulation part to verify the effectiveness of the proposed control scheme.

FLOATING QUANTIZATION EFFECTS ON MULTIRATE SAMPLED-DATA NONLINEAR CONTROL SYSTEMS

In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.