Observability conditions of switched linear singular systems

The observability problem of switched linear singular(SLS) systems is studied in this paper. Based on the observability definition, the unobservable subspaces of given switching laws are investigated under the condition that all subsystems are regular. A necessary condition and a sufficient condition for observability of SLS systems are given. It is shown that the observability and controllability are dual for some special SLS systems with circulatory switching laws. The method developed here is applicable to the observability analysis of normal switched linear systems.     

切换线性奇异系统输出反馈容许控制

The admissibility analysis and robust admissible control problem of the uncertain discrete- time switched linear singular (SLS) systems for arbitrary switching laws are investigated. Based on linear matrix inequalities, some sufficient conditions are given for: A) the existence of generalized common Lyapunov solution and the admissibility of the SLS systems for arbitrary switching laws, B) the existence of static output feedback control laws ensuring the admissibility of the closed-loop SLS systems for arbitrary switching laws and norm-bounded uncertainties.     

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.     

Critical dwell time of switched linear systems

In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable （While some switching models are probably unstabilizable）, an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition, algorithms for designing switching laws and controls are presented.     

Critical dwell time of switched linear systems

In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable (While some switching models are probably unstabilizable), an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition, algorithms for designing switching laws and controls are presented.     

切换线性超循环系统的稳定性分析

超循环---生物学中重要模型, 具有广泛的实际背景. 本文将超循环系统扩展为切换超循环系统. 循环矩阵的循环结构为研究切换超循环系统的稳定性提供了有效的方法, 给出切换线性时变超循环系统在任意切换律下渐近稳定的充要条件和切换线性定常超循环系统可切换镇定的充分条件.     

Nonpathological sampling of switched linear systems

We study the conservation of observability after sampling for the class of switched linear systems with no inputs and switching in the measurement equation only. Using van der Waerden's Theorem, a classic result from Ramsey Theory, we give a sufficient condition on the components of the resulting discretized switched linear system for it to be observable under arbitrary switching sequences. This preliminary result then enables us to extend the Kalman-Bertram criterion for nonpathological sampling to the class of switched linear systems under consideration.     

Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results

During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here.      

线性混合系统的可观性分析

线性混合系统的控制输入(包括离散控制和连续控制)会影响混合系统的状态可观性．混合系统的可观性包括初始的离散状态和连续状态，以及离散状态的切换时间．对此．分析了系统的控制输入对线性混合系统状态(主要是离散状态)的影响，并论述这将有助于改善某些线性混合系统状态的可观性．通过分析给出了在这种情形下比较宽松的线性混合系统状态可观性条件及其秩检验条件，并给出说明性示例．     

一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题. 首先, 给出保证线性部分有一致规范型的充分条件. 其次, 利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定. 最后, 通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.     

Observer-based robust H-infinity control for uncertain switched systems

The problem of observer-based robust H-infinity control is addressed for a class of linear discrete-time switched systems with time-varying norm-bounded uncertainties by using switched Lyapunov function method. None of the individual subsystems is assumed to be robustly H-infinity solvable. A novel switched Lypunov function matrix with diagonal-block form is devised to overcome the difficulties in designing switching laws. For robust H-infinity stability analysis, two linear-matrix-inequality-based sufficient conditions are derived by only using the smallest region function strategy if some parameters are preselected. Then, the robust H-infinity control synthesis is studied using a switching state feedback and an observer-based switching dynamical output feedback. All the switching laws are simultaneously constructively designed. Finally, a simulation example is given to illustrate the validity of the results.     

Two slow stabilizing switching laws for discrete time positive switched systems

On the basis of a linear copositive Lyapunov function (LF) and a diagonal quadratic LF, respectively, two slow stabilizing switching laws are proposed for discrete time positive switched systems composed of subsystems. Under these two stabilizing switching laws, the LFs are allowed to increase in state‐driven intervals while the stability of positive switched systems is maintained. In addition, it is shown that positive switched systems under these two slow switching laws are robust against certain classes of perturbations. Furthermore, when the states of the systems are not available, observer‐based stabilizing switching laws for positive switched systems are also proposed. Some numerical examples are finally given to illustrate the effectiveness of the proposed stabilizing switching laws. Copyright © 2013 John Wiley & Sons, Ltd.     

一类不确定离散切换模糊组合系统的稳定性控制

以模糊T-S模型对离散切换组合系统的研究模型进行重新构建,分别利用单Lyapunov函数方法设计出分散切换律和控制器,给出了利用矩阵不等式表达的系统在分散切换律和分散控制器作用下的可镇定条件,仿真结果表明了该方法的有效性。     

切换对称组合系统的稳定性

首次提出了切换对称组合系统的概念, 研究了此类系统在任意切换下渐近稳定的条件, 同时分别利用多李雅普诺夫函数方法和单李雅普诺夫函数方法, 给出使切换对称组合系统渐近稳定的切换律, 利用切换对称组合系统的结构特点, 使其切换律的设计条件得到简化.     

凸锥型不确定线性切换系统的二次镇定

研究具有凸锥型不确定性的线性切换系统的二次鲁棒稳定化问题.这种不确定性是由若干已知常数矩阵所张成的凸锥构成的.利用凸组合技术,分别给出了连续和离散线性切换系统的鲁棒二次可稳定条件及切换律的设计方法.按照这些条件,只要判断张成凸锥的顶点矩阵的某个凸组合是否可稳即可.最后给出仿真例子.     

Robust estimation algorithm for both switching signal and state of switched linear systems

We present a hybrid-type observer for detecting the switching time and estimating both the active mode and the states of continuous-time switched linear systems. The systems under consideration have external inputs and are affected by unknown disturbances. In addition, noise corrupts the output measurements. In this setting the switching cannot be detected immediately, and thus, this paper presents a condition that relates the amount of delay to the sizes of the unknown disturbances/noises, the external inputs, and the states, and the strength of the observability. Once the condition is satisfied, the proposed observer and algorithm return the exact active mode and approximate state information of the switched system. A numerical example is also presented to show the performance of our algorithm..     

切换线性系统的聚合优化

分析了切换线性系统的稳定性和优化问题,提出了一个Armijo步长优化的共轭梯度算法来寻找适当代价函数下的优化切换时间点集.为了确保优化切换路径是可压缩的,提出了代价函数需要满足的受限表达式.设计了几种优化分段状态反馈切换律来搜索聚合系统的最优切换路径,同时这些切换路径就是对应原始切换线性系统的次优化切换路径.最后,一个实例演示了不同切换律下的切换策略和优化代价.     

一类混合动态系统的能控性和能观性研究

针对一类混合动态系统———周期型线性切换系统, 给出系统能控性、能观性的充分必要条件, 并通过例子加以验证.     

一类混合动态系统的能控性和能观性研究

针对一类混合动态系统--周期型线性切换系统,给出系统能控性、能观性的充分必要条件,并通过例子加以验证.     

一类不确定切换系统的鲁棒状态反馈镇定

研究了一类扰动项不满足匹配条件的不确定切换系统的鲁棒镇定问题.在每个子系统均不能镇定的情况下,利用完备性条件和多李雅普诺夫函数方法,分别得到了不确定切换系统可镇定的充分条件.状态矩阵和控制输入矩阵同时带有时变、未知且有界的不确定性,基于凸组合技术和LMI方法,设计出鲁棒状态反馈控制器及相应的切换策略,使得闭环系统在其平衡点处是渐近稳定的.最后仿真结果表明所设计的控制器及切换策略的正确有效性.