切换系统输入对状态稳定性的充分条件

研究了切换系统输入对状态的稳定性.在所有子系统都是输入对状态稳定的条件下,利用各子系统的KY函数和K函数构造出切换系统所需的KY函数和X函数,从而给出了切换系统输入对状态稳定的充分条件.对于一类常见的切换系统,计算出保证输入对状态稳定性的切换停留时间的下界,所有结果都是构造性的.     

Lyapunov Conditions for Finite-Time Input-to-State Stability of Impulsive Switched Systems

<正>Dear Editor,This letter studies finite-time input-to-state stability (FTISS) for impulsive switched systems. A set of Lyapunov-based conditions are established for guaranteeing FTISS property. When constituent modes governing continuous dynamics are FTISS and discrete dynamics involving impulses are destabilizing, the FTISS can be retained if impulsive-switching signals satisfy an average dwell-time(ADT) condition.     

Necessary and Sufficient Conditions for the Passivicability of Linear Distributed Systems

For a wide class of systems, as is known, hyper-minimal phase is necessary and sufficient for the strict passivicability of a system. This class contains both concentrated- and distributed-parameter systems, including parabolic equations that describe heat-exchange and diffusion processes. Our results are applicable to finite-dimensional input and output spaces, which are important for application and cover systems with different numbers of inputs and outputs for which passivity is superseded by the G-passivity of some rectangular matrix G. An example of a diffusion-type one-dimensional partial differential equation directly containing control is given. Proofs are based on the infinite-dimensional variant of the Yakubovich–Kalman lemma and Nefedov–Sholokhovich exponential stabilization theorem.     

Necessary and Sufficient Conditions for Consensus in Third Order Multi-Agent Systems

We deal with a consensus control problem for a group of third order agents which are networked by digraphs. Assuming that the control input of each agent is constructed based on weighted difference between its states and those of its neighbor agents, we aim to propose an algorithm on computing the weighting coefficients in the control input. The problem is reduced to designing Hurwitz polynomials with real or complex coefficients. We show that by using Hurwitz polynomials with complex coefficients, a necessary and sufficient condition can be obtained for designing the consensus algorithm. Since the condition is both necessary and sufficient, we provide a kind of parametrization for all the weighting coefficients achieving consensus. Moreover, the condition is a natural extension to second order consensus, and is reasonable and practical due to its comparatively decreased computation burden. The result is also extended to the case where communication delay exists in the control input.      

延时系统输入状态稳定性的Lyapunov逆理论

研究了延时系统输入状态稳定性的局部Lipschitz连续的Lyapunov逆理论. 针对含有任意可测局部本质有界扰动的延时系统, 一个局部Lipschitz连续的Lyapunov泛函被证实是存在的, 如果该系统是鲁棒渐进稳定的. 根据该结论, 延时系统输入状态稳定性的Lyapunov特征被进一步得到.     

Algebraic Necessary and Sufficient Conditions for the Controllability of Conewise Linear Systems

The problem of checking certain controllability properties of even very simple piecewise linear systems is known to be undecidable. This paper focuses on conewise linear systems, i.e., systems for which the state space is partitioned into conical regions and a linear dynamics is active on each of these regions. For this class of systems, we present algebraic necessary and sufficient conditions for controllability. We also show that the classical results of controllability of linear systems and input-constrained linear systems can be recovered from our main result. Our treatment employs tools both from geometric control theory and mathematical programming.     

滞后动态系统广义指数稳定的充要条件

本语文针对一般的滞后动态系统建立了广义指数稳定性的充分和必要条件，并由所建立的充要条件得出了系统过渡过程的时变指数衰减估计，作为所建结果的应用，基于矩阵工给出了一类滞后动态系统过渡过程的相应指数衰减估计，本文揭示了所建衰减估计可好于那些仅基于充分稳定性条件所得的估计。     

二阶线性切换系统指数镇定的充要条件

考虑二阶切换系统的镇定问题. 基于极坐标表示, 揭示了由锥形区域所界定的切换控制与子系统几何性质之间的自然联系. 由此, 建立了可镇定的充分必要条件; 并从代数与几何两方面刻画了镇定切换控制的特征. 进而给出了状态轨线指数收敛率的估计, 并阐释了由切换产生极限环与滑模运动的机理. 数值例子详细说明了结论的有效性.     

Necessary and Sufficient Conditions for the Absolute Stability of Two-Dimensional Time-Varying Systems

Easily verifiable necessary and sufficient conditions for the absolute stability of two-dimensional time-varying systems are derived with a modified method of comparison of two-dimensional systems.__________Translated from Avtomatika i Telemekhanika, No. 7, 2005, pp. 43–53.Original Russian Text Copyright © 2005 by Leonov.     

Necessary and Sufficient Conditions for Consensus of Delayed Fractional‐order Systems

In this paper, we study the consensus problem of fractional‐order systems with input delays. Using Laplace transform method, the stability of the fractional‐order systems is first discussed in the frequency domain. Based on the generalized Nyquist stability criterion, a necessary and sufficient condition is further derived to ensure the consensus of fractional‐order systems with identical input delays over directed interaction topology. Furthermore, when the interaction topology is undirected, the consensus condition of fractional‐order systems with heterogeneous input delays is explicitly given. Finally, some illustrative examples are presented to show the effectiveness and advantages of the theoretical results.     

Lyapunov Functions, Stability and Input-to-State Stability Subtleties for Discrete-Time Discontinuous Systems

In this note we consider stability analysis of discrete-time discontinuous systems using Lyapunov functions. We demonstrate via simple examples that the classical second method of Lyapunov is precarious for discrete-time discontinuous dynamics. Also, we indicate that a particular type of Lyapunov condition, slightly stronger than the classical one, is required to establish stability of discrete-time discontinuous systems. Furthermore, we examine the robustness of the stability property when it was attained via a discontinuous Lyapunov function, which is often the case for discrete-time hybrid systems. In contrast to existing results based on smooth Lyapunov functions, we develop several input-to-state stability tests that explicitly employ an available discontinuous Lyapunov function.     

Explicit Necessary and Sufficient Conditions for Quadratic Linearization

The existing necessary and sufficient conditions for quadratic linearization of control affine systems are in effect, constructive in nature. The exception is the classical result, which requires one to check involutive properties of distributions of the quadratic polynomials to be linearized. Nevertheless, the latter condition is difficult to verify. In this paper, we provide necessary and sufficient conditions for quadratic linearization that are not constructive but are based on checking a linear system of equations involving quadratic polynomial terms only. The system needs only to be put in controller normal form of the linear part which is known. Thus, the result is verifiable and explicit. Also, if required, once the quadratic linearization conditions are met, we show how to construct the coordinate and state feedback transformation to implement the linearization.     

线性时滞系统稳定的充分必要条件

提出一个新的线性时滞系统稳定的充分必要条件,与以前的结论不同的是,我们的结论的表达形式更容易数值计算。开发相应的二种收敛算法,解决系统时滞独立稳定判断和时滞相关稳定的时滞界估计。本文给出范数有界不确定性时,系统稳定的充分条件。文末给出的数值实例证明本文结果降低计算复杂度,改进了时滞估计保守性。     

限制解耦控制的充分必要条件*

本文利用初等变换方法推得非方系统限制解耦控制的充分必要条件。     

Necessary and Sufficient Conditions for Dynamical Structure Reconstruction of LTI Networks

This paper formulates and solves the network reconstruction problem for linear time-invariant systems. The problem is motivated from a variety of disciplines, but it has recently received considerable attention from the systems biology community in the study of chemical reaction networks. Here, we demonstrate that even when a transfer function can be identified perfectly from input–output data, not even Boolean reconstruction is possible, in general, without more information about the system. We then completely characterize this additional information that is essential for dynamical reconstruction without appeal to ad-hoc assumptions about the network, such as sparsity or minimality.      

采用线性不定方程组的Hamiltonian存在判定条件

本文基于{0，1}线性不定方程组和顶边关联矩阵．提出了一个基于无向Hamiltonian图的充要判定定理。并证明了满足该定理的不定方程组解向量对应给定圄的Hamiltonian回路中边的集合，本文还推导出两个可以基于矩阵秩的Hamiltonian回路存在的必要判据。     

A Necessary and Sufficient Frequency Domain Criterion for the Passivity of SISO Sampled-Data Systems

We present a frequency domain solution to the sampled-data passivity problem. Our analysis is exact in the sense that we take into account the intersample behavior of the system. We use frequency response (FR) operators to first obtain necessary conditions on the sampling rate $T$ and the relative degree of the open-loop transfer function $G_{11}$ for achieving a passive continuous-time closed-loop system. Then, assuming passivity of $G_{11}$ and closed-loop stability, we derive a necessary and sufficient condition for discrete-time controllers that render a passive closed-loop system. We apply the obtained results to the problem of stability of haptic systems.      

并行分组交换中负载平衡充要条件的分析

负载平衡是并行分组交换(PPS-parallelpacketswitch)结构的一项关键技术,该文对带缓存PPS结构中负载平衡的充要条件进行了研究。首先基于守恒原理建立流体并行交换的流量守恒方程,并分析流体并行交换中负载平衡的充要条件,在此基础上建立PPS的流量守恒方程,并定义PPS负载平衡,分析PPS负载平衡算法应该满足的充要条件。     

线性时滞系统时滞独立稳定的充分条件

利用Lyapunov稳定性理论，通过一个推广的Lyapunov矩阵方程得出时滞独立稳定的充分条件，基于这个充分条件建立了几个判定线性时滞系统稳定性的简单判据，并推导出系统具有任意指定收敛速度指数稳定的充分条件。计算例子说明了所得结果的有效性。     

Necessary and Sufficient Condition for Global Controllability of Planar Affine Nonlinear Systems

In this correspondence, we will investigate the global controllability of general planar affine nonlinear systems, and present a simple necessary and sufficient condition for global controllability. The analysis is carried out in detail, which is based on some basic facts in planar topology such as the Jordan curve Theorem, and in the geometrical theory of ordinary differential equations including the Poincare-Bendixson Theorem. Furthermore, we will also discuss the global controllability for higher dimensional affine nonlinear system with a triangular-like structure.