Schwarz lemma for driving point impedance functions and its circuit applications

In this paper, a boundary version of the Schwarz lemma is investigated for driving point impedance functions and its circuit applications. It is known that driving point impedance function, Z(s) = 1 + c_p(s − 1)^p + c_{p + 1}(s − 1)^{p + 1} + ..., p > 1, is an analytic function defined on the right half of the s-plane. Two theorems are presented using the modulus of the derivative of driving point impedance function, |Z′(0)|, by assuming the Z(s) function is also analytic at the boundary point s = 0 on the imaginary axis with . In the obtained inequalities, the value of the function at s = 1 and the derivatives with different orders have been used. Finally, the sharpness of the inequalities obtained in the presented theorems is proved. Simple LC circuits are obtained using the obtained driving point impedance functions.     

Synchronisation of a class of networked passive systems with switching topology

This article considers the output synchronisation of a class of networked agents. Each agent is a passive system. Local information, used by each agent to adjust its movement, forms a network with switching adjacent topology. First, we consider the asymptotic stability of switched non-linear time-varying systems with delayed measurement feedback by using multiple Lyapunov function. A Barbalat-like lemma is obtained. Then the result is applied to the output synchronisation of a class of networked passive systems with switching topology. A verifiable sufficient condition is presented.     

State‐space characterization of all solutions to a positive real control problem

Abstract

The purpose of this paper is to give a state‐space characterization of all internally stabilizing finite‐dimensional linear time‐invariant output feedback controllers for a given finite‐dimensional linear time‐invariant plant which ensure that the resulting closed‐loop transfer function is extended strictly positive real(ESPR). All such controllers are parameterized by a fixed linear fractional transformation with an ESPR, stable free parameter. The parameterized controllers have a state dimension not less than that of the open‐loop plant. The development uses only elementarily algebraic ideas beginning with a change of variables, an extended version of Kalman‐Yacubovich‐Popov positive real lemma, and Youla parameterization, thus the proofs given are simple and clear.     

可交换上下文无关文法

本文提出了可交换上下文无关文法及其该文法产生的语言——可交换上下文无关语言,证明了正规语言类是可交换上下文无关语言类的一个子集,而可交换上下文无关语言类是上下文无关语言类的一个子集;讨论了可交换上下文无关语言的结构特点,并给出了可交换上下文无关语言的Pumping引理。     

Some functional inequalities and inclusion relationships associated with certain families of integral operators

By making use of certain familiar integral operators, the authors introduce and investigate several new subclasses of starlike, convex, close-to-convex, and quasi-convex functions. Among other results presented here, the authors establish a number of inclusion relationships associated with some of these integral operators. Some of the results established in this paper would provide extensions of those given in earlier works.     

On control for linear systems with interval time-varying delay

This paper deals with the problem of delay-dependent robust H_∞ control for linear time-delay systems with norm-bounded, and possibly time-varying, uncertainty. The time-delay is assumed to be a time-varying continuous function belonging to a given interval, which means that the lower and upper bounds for the time-varying delay are available, and no restriction on the derivative of the time-varying delay is needed, which allows the time-delay to be a fast time-varying function. Based on an integral inequality, which is introduced in this paper, and Lyapunov–Krasovskii functional approach, a delay-dependent bounded real lemma (BRL) is first established without using model transformation and bounding techniques on the related cross product terms. Then employing the obtained BRL, a delay-dependent condition for the existence of a state feedback controller, which ensures asymptotic stability and a prescribed H_∞ performance level of the closed-loop systems for all admissible uncertainties, is proposed in terms of a linear matrix inequality (LMI). A numerical example is also given to illustrate the effectiveness of the proposed method.     

STOCHASTIC STABILIZATION AND H∞ CONTROL FOR DISCRETE JUMPING SYSTEMS WITH TIME DELAYS

In this paper, robust stochastic stabilization and H_∞ control for a class of uncertain discrete‐time linear systems with Markovian jumping parameters are considered. Based on a new bounded real lemma derived upon an inequality recently proposed, a new iterative state‐feedback controller design procedure for discrete time‐delay systems is presented. Sufficient conditions for stochastic stabilization are derived in the form of linear matrix inequalities (LMIs) based on an equivalent model transformation, and the corresponding H_∞ control law is given. Finally, numerical examples are given to illustrate the solvability of the problems and effectiveness of the results.     

利用GRONWALL定理确定高维非线性电路唯一稳态

本文利用GRONWALL定理 ,确定了电路的唯一稳态新条件。本文的结果对电路元件的约束 ,仅要求其成份关系斜率有界即可。这大大放松了目前已有的经典结果中要求电路元件斜率为正的限制 ,扩展了已有的结果。     

基于预测-校核机制的发电侧煤电联动

通过引入用于预测普通商品价格的较成熟的几何布朗运动模型建立了燃煤市场的煤价波动模型。通过分析火电企业生产成本与煤价之间的关系，依据Ito引理将燃煤市场的煤价波动引入电厂生产成本的波动中，建立了电厂生产成本的波动模型。通过求取一段时间内电厂生产成本的波动期望值，对政府职能部门提出了依据该期望值对电厂上网电价进行调整的建议。考虑到政府职能部门提前对电厂上网电价进行调整可能存在风险的实际情况，提出了构建煤电联动预测&;#65533;校核机制的思路，为上述模型的应用提供了保障。最后举例说明了该模型的使用步骤并验证了其合理性与可行性。     

Mixed output feedback of the finite frequency H∞ control for singularly perturbed system

This paper considers the H_∞ control problem for a class of linear singularly perturbed systems in the finite frequency range. A mixed output feedback controller comprising of a static output feedback controller and a dynamic output feedback controller is developed for the system stabilisation. Based on the generalised Kalman–Yakubovich–Popov (GKYP) lemma, the frequency-domain inequalities can be converted into linear matrix inequalities which are numerically tractable. Compared with the existing full frequency approaches, better results are obtained. Moreover, the selection methods of the cut-off frequencies in both low and high frequency ranges are extensively studied with a view to reduce the conservativeness in output feedback control design. Simulation results suggest the asymptotic validity of the main results in this paper.