The Analysis of Global Input-to-state Stability for Piecewise Affine Systems with Time-delay

In this paper, global input-to-state stability （ISS） for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lyapunov-Krasovskii methods are used The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown respectively.

Input-to-state stability of Euler-Maruyama method for stochastic delay control systems

This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical methods is established.The conditions of the exact and EM method for an SDCS with the property of mean-square exp-ISS are obtained without involving control Lyapunov functions or functional.Under the global Lipschitz coefficients and mean-square continuous measurable inputs,it is proved that the mean-square exp-ISS of an SDCS holds if and only if that of the EM method is preserved for a sufficiently small step size.The proposed results are evaluated by using numerical experiments to show their effectiveness.

Input-to-State Stabilization of Nonlinear Impulsive Delayed Systems: An Observer-Based Control Approach

This paper addresses the problems of input-to-state stabilization and integral input-to-state stabilization for a class of nonlinear impulsive delayed systems subject to exogenous dis-turbances.Since the information of plant’s states,time delays,and exogenous disturbances is often hard to be obtained,the key design challenge,which we resolve,is the construction of a state observer-based controller.For this purpose,we firstly propose a corresponding observer which is independent of time delays and exogenous disturbances to reconstruct(or estimate)the plant’s states.And then based on the observations,we establish an observer-based control design for the plant to achieve the input-to-state stability(ISS)and integral-ISS(iISS)properties.With the help of the comparison principle and average impulse interval approach,some sufficient conditions are presented,and moreover,two different linear matrix inequalities(LMIs)based criteria are proposed to design the gain matrices.Finally,two numerical examples and their simulations are given to show the effectiveness of our theoretical results.

带干扰项的ARZ交通流模型的时滞控制与ISS稳定性

针对线性化之后的ARZ交通流模型,已有文献通常基于如下假设:一是系统的平衡态恰好等于自由流的速度,二是进入上游路段的交通量恰好等于交通需求的数学期望,三是边界反馈不考虑时滞因素的影响.该文抛开各类限制条件,结合时滞边界控制策略,建立了具有模型漂移项和边界扰动项的PDE-PDE无穷维耦合闭环系统.具体地,采用算子半群理论,将闭环系统改写为抽象发展方程的形式;结合线性系统解与控制算子的允许性理论,证明了闭环系统的适定性;构造加权ISS-Lyapunov函数,证明了闭环系统的输入-状态稳定性(ISS),得到了反馈参数的耗散性条件.通过数值仿真实验,进一步验证本文设计的时滞控制器的有效性与参数条件的可行性.

Input-to-State Stability for Impulsive Switched Singular Systems with Mismatched Disturbances

This work investigates the input-to-state stability(ISS)problem for impulsive switched singular systems(ISSSs)with mismatched disturbances.In this paper,‘disturbance’is a general concept that includes model uncertainty,unknown system dynamic,external disturbance,etc.The modified uncertainty and disturbance estimator(UDE)-based control method is presented for singular systems and ISSSs,a virtual control is introduced to offset the effects of mismatched disturbances.On the basis of a discontinuous multiple Lyapunov functional and admissible edge-dependent average dwell time(AED-ADT)method,several sufficient conditions in terms of linear matrix inequalities(LMIs)are obtained to ensure that the closed-loop systems are regular,impulse-free and ISS.Finally,two examples are given to demonstrate the effectiveness of the proposed results.

Chaos Synchronization of Nonlinear Bloch Equations Based on Input-to-State Stable Control

In this paper, we propose a new input-to-state stable （ISS） synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality （LMI） approach, for the first time, the ISS synchronization controller is presented to not only guarantee the asymptotic synchronization but also achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed synchronization scheme.

Input-to-state stability and gain computation for networked control systems

This paper studies the stability problem for networked control systems.A general result,called network gain theorem,is introduced to determine the input-to-state stability(ISS)for interconnected nonlinear systems.We show how this result generalises the previously known small gain theorem and cyclic small gain theorem for ISS.For the case of linear networked systems,a complete characterisation of the stability condition is provided,together with two distributed algorithms for computing the network gain:the classical Jacobi iterations and a message-passing algorithm.For the case of nonlinear networked systems,characterisation of the ISS condition can be done using M-functions,and Jacobi iterations can be used to compute the network gain.

Estimation of LISS(local input-to-state stability) properties for nonlinear systems

Compared with input-to-state stability(ISS) in global version,the concept of local input-to-state stability(LISS) is more relevant and meaningful in practice.The key of assessing LISS properties lies in investigating three main ingredients,the local region of initial states,the local region of external inputs and the asymptotic gain.It is the objective of this paper to propose a numerical algorithm for estimating LISS properties on the theoretical foundation of quadratic form LISS-Lyapunov function.Given developments of linear matrix inequality(LMI) methods,this algorithm is effective and powerful.A typical power electronics based system with common DC bus is served as a demonstration for quantitative results.

ISS加固土的微观结构及强度特征

通过化学分析、SEM电镜扫描分析、无侧限抗压强度等实验 ,研究了ISS加固粉土质砂和砂质低液限粉土的微观结构及其强度特征 .结果表明 :ISS的掺入 ,使土体易于压实 ,孔隙体积减小 ,密实度提高 ,从而提高土的强度 .ISS加固土中适量掺入水泥 ,可以明显提高加固土的早期强度 ,且能生长出纤维状矿物 ,充填在土颗粒之间的孔隙中 。

ISS 土壤稳定剂路用性能的试验研究

通过室内试验并结合试验路的使用情况，确定了靖边土、安塞土、西安土三种土样在最佳含水量下的ＩＳＳ剂最佳用量，由此分析了ＩＳＳ剂对三种土的抗压强度、抗折强度、水稳性的改良效果，进而对ＩＳＳ土壤稳定剂的路用性能进行了一定的分析评价。

ISS土壤固化剂在渠道防渗中的试验研究

利用电离子土壤固化剂 (IonicSoilStabilizer ,简称ISS)、石灰和砂加固湛江市志满水库的含砂高液限粉土(MHS) ,通过试验得出最优配合比。ISS加固土具有强度高、水稳定性好、抗渗透能力强等优点 ,它既是气硬性材料 ,又是水硬性材料。ISS加固土渠拌法施工比厂拌法施工简便 ,可就地取材。

ISS-水泥联合固化淤泥的力学特性研究

采用离子土固化剂(ISS)和水泥对宁德海相淤泥进行化学固化,通过阿太堡试验确定最优ISS体积比;通过7 d龄期无侧限抗压强度试验确定临界水泥掺量。针对酸碱固化剂共存对淤泥固化的影响,对淤泥固化样品进行了物理、力学试验,分别研究酸性ISS、碱性水泥、NaOH碱化剂等单掺和复掺固化淤泥的力学特性及固化效果,探讨固化剂之间的影响机理。试验结果表明:酸性ISS与水泥之间相互抑制,ISS溶液中H+阻碍了水泥的水化进程,降低了固化土强度;NaOH碱化ISS和水泥联合固化淤泥与单掺水泥相比,不但弥补了水泥提高早期强度缓慢的不足,而且可节约大约3%的水泥用量。

ISS—水泥联合固化淤泥的微观机理研究

采用离子土固化剂(ISS)、水泥、碱化剂NaOH对福建宁德海相淤泥进行单掺、复掺、碱化复掺等不同方式的化学固化。在对固化前后的淤泥样品开展无侧限抗压强度、24h固结压缩等力学试验的基础上,通过SEM、XRD、XRF等微观测试,分析不同固化方式下淤泥的固化效果;研究不同形态酸、碱固化剂相互作用的定性和定量关系;探讨ISS—水泥联合固化淤泥的微观机理。试验结果表明:在相同水泥掺量下,NaOH碱化ISS—水泥联合固化淤泥效果优于单掺水泥固化淤泥效果,且二者都好于酸性ISS—水泥联合固化淤泥的效果。

一类带不确定输入动态非线性系统的鲁棒ISS镇定

用ISS镇定方法研究了一类带不确定输入动态受扰非线性系统的干扰抑制问题 。

A Notion of Stochastic Input-to-State Stability and Its Application to Stability of Cascaded Stochastic Nonlinear Systems

In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of （practical） stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, （a） an （practical） SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded （practical） SISS subsystems.

Input-to-State Stability of Switched Nonlinear Delay Systems Based on a Novel Lyapunov-Krasovskii Functional Method

In this paper, the input-to-state stability （ISS） analysis is addressed for switched nonlinear delay systems. By introducing a novel Lyapunov-Krasovskii functional with indefinite derivative and the merging switching signal techniques, some new- criteria are established for switched nonlinear delay systems under asynchronous switching, which extends the existing results to the nonlinear systems with switching rules and delays. The ISS problem is also considered under synchronous switching for switched nonlinear systems by employing the similar techniques. Finally, a nonlinear delay model is provided to show the effectiveness of the proposed results.

Input-to-state stability of switched nonlinear systems

The input-to-state stability （ISS） problem is studied for switched systems with infinite subsystems. By using multiple Lyapunov function method, a sufficient ISS condition is given based on a quantitative relation of the control and the values of the Lyapunov functions of the subsystems before and after the switching instants. In terms of the average dwell-time of the switching laws, some sufficient ISS conditions are obtained for switched nonlinear systems and switched linear systems, respectively.

Adaptive stabilization for cascade nonlinear systems

An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov function (CLF) techniques. We show that unknown bounded disturbance can be estimated by update laws, which requires less information on unknown disturbance, as a part of stabilizing control. The design method achieves the desired property: global robust stability. Our contribution is illustrated with the example of a disturbed pendulum.