离散系统降阶H∞控制器的设计

针对离散控制系统,研究其降阶H∞控制器设计方法.首先,采用线性矩阵不等式方法,给出离散系统状态反馈H∞控制器存在的条件;利用离散系统H∞控制器可解的条件,研究离散系统的降维观测器设计方法;通过设计系统的降维观测器,使降维观测器的观测输出和系统的状态反馈输入误差趋于零,以降阶观测器的输出作为系统的控制输入,使闭环控制系统...     

基于有限时间稳定的含不确定性离散切换系统控制

针对一类含有不确定性的离散时间切换系统,研究了该类切换系统的有限时间稳定性问题。通过构造类Lyapunov函数和利用线性矩阵不等式的方法,给出了在任意切换序列条件下,能够使含不确定性的离散时间切换系统满足有限时间稳定的一个充分条件,在所给定理的基础上,对于该类切换系统进行有限时间控制,给出了使其可保持有限时间稳定的切换状态反馈控制器设计方法。最后,通过一个数值算例仿真验证了所提出方法的有效性和可行性。     

离散时间非线性系统的观测器设计

针对离散时间Lipschitz非线性系统的观测器设计问题,依据离散时间系统的Lyapunov稳定性理论,研究了保证观测误差渐近稳定的充分条件,并依据该条件应用线性矩阵不等式方法,得到了观测器增益矩阵的设计方法。所得方法计算简便,并通过算例说明该方法的应用。     

异步电机全阶磁链观测器反馈矩阵设计

异步电机全阶磁链观测器是以电机本身作为参考模型,通过构建状态方程观测电机的磁链与定子电流。它将定子电流作为输出,引入实际电流与观测电流的误差作为反馈校正,通过调整校正项的反馈矩阵增益,改善全阶磁链观测器的性能。全阶磁链观测器的反馈矩阵设计从磁链模型切换策略与转速辨识动态特性两方面进行。全阶磁链观测器的特征函数表示磁链观测器在电流模型磁链观测器与电压模型磁链观测器之间切换的平滑程度;从双时间角度出发,全阶磁链观测器可以分解为转速辨识系统与磁链观测系统。在深入分析反馈矩阵对全阶磁链观测器的特征函数以及转速辨识动态特性的基础上,提出一种改善全阶磁链观测器平滑切换与全阶磁链观测器转速辨识动态特性的反馈矩阵设计方法。仿真和物理实验验证了分析方法的正确性与所提对策的可行性。     

一类不确定线性离散系统有限时间观测器设计

针对一类不确定线性离散系统有限时间观测器最优设计问题,利用线性矩阵不等式方法以及有限时间有界的概念,给出了具有不确定外部扰动输入的线性离散系统有限时间有界的充分条件.对具有状态反馈和输出的线性不确定离散系统引入有限时间观测器的概念,可以保证在给定的有限时间区间内,观测误差小于一个给定的界,并给出了最优有限时间观测器的具体设计方案.此方案的有效性可以通过仿真实验得到验证.     

一类切换线性中立时滞系统稳定性的分析

提出了切换中立时滞系统的概念.研究了线性切换中立时滞系统渐近稳定性问题,并分别利用单Lyapunov函数法和多Lyapunov函数法,以线性矩阵不等式的形式分别给出一类切换线性中立时滞系统渐近稳定的充分条件及切换律的设计.然后假设存在有限个备选的控制增益已知的控制器,并在任何单一的状态反馈控制器都不能镇定系统时,设计该类系统的混杂状态反馈控制器,使闭环系统渐近稳定.最后用部分元件等效电路（PEEC）的仿真例子验证了结论的有效性.     

采样系统快时变扰动比例积分观测器鲁棒H2/H∞控制

针对控制系统存在快时变扰动或噪声使传统观测器存在较大观测误差问题,依据鲁棒控制理论,采用线性矩阵不等式(LMI)方法,设计鲁棒H2/H∞全维状态比例积分观测器.研究系统在快时变扰动情况下,采样系统基于改进比例积分观测器的状态观测效果及鲁棒稳定性,得到一类充分条件,给出快时变扰动观测器比例增益、积分增益、控制器增益以及鲁棒H2性能指标的求解方法.仿真结果表明:所设计的观测器鲁棒性强,提高了状态观测精确度.     

采样系统慢时变扰动比例积分观测器鲁棒控制

针对控制系统存在扰动或噪声使传统观测器存在较大观测误差问题,依据鲁棒控制理论,采用线性矩阵不等式(LMI)方法,设计了鲁棒H2/H∞全维状态比例积分观测器。研究了系统存在慢时变扰动情况下,采样系统基于比例积分观测器的状态观测效果及鲁棒稳定性,得到了一类充分条件,给出了观测器比例增益、积分增益、控制器增益以及鲁棒H2性能指标的求解方法。仿真结果表明,所设计的观测器计算量小,鲁棒性强,提高了状态观测精确度。     

离散多时滞系统多故障模式下的H_∞容错控制

针对状态具有多个时滞的线性离散时间系统,基于Lyapunov稳定性理论和线性矩阵不等式方法（LMI）,分别采用无时滞记忆和有时滞记忆的状态反馈控制律,研究了执行器和传感器同时发生故障的情况下,离散多时滞系统的H∞容错控制问题。首先给出了系统没有干扰输入时存在无时滞记忆状态反馈容错控制器的一个充分条件;进一步,给出了在H∞扰动衰减指标约束下,系统存在无时滞记忆状态反馈H∞容错控制器的一个充分条件;并将结论推广到设计有时滞记忆的状态反馈容错控制器的情况。最后,仿真结果证明了所得H∞容错控制器设计方法的正确性和有效性。     

基于自适应观测器的感应电机无速度传感器DTC系统的仿真

在Matlab/Simulink下搭建了一个基于自适应观测器的感应电机无速度传感器直接转矩控制(direct torque control,DTC)系统仿真平台,建立了鲁棒自适应全阶状态观测器并给出了基于鲁棒观测器的速度辨识律.应用Lyapunov稳定性理论,观测器的增益借助于Matlab中的LMI工具箱求解线性矩阵不等式得到.仿真结果表明该模型具有很好的稳态性能,并具有良好的鲁棒性.     

Non‐minimum phase switched systems: HOSM‐based fault detection and fault identification via Volterra integral equation

In this paper, the problem of continuous and discrete state estimation for a class of linear switched systems with additive faults is studied. The class of systems under study can contain non‐minimum phase zeroes in some of their ‘operating modes’. The conditions for exact reconstruction of the discrete state are given using structural properties of the switched system. The state space is decomposed into the strongly observable part, the non‐strongly observable part, and the unobservable part, to analyze the effect of the unknown inputs. State observers based on high‐order sliding mode to exactly estimate the strongly observable part and Luenberger‐like observers to estimate the remaining parts are proposed. For the case when the exact estimation of the state cannot be achieved, the ultimate bounds on the estimation errors are provided. The proposed strategy includes a high‐order sliding‐mode‐based fault detection and a fault identification scheme via the solution of a Volterra integral equation. The feasibility of the proposed method is illustrated by simulations. Copyright © 2013 John Wiley & Sons, Ltd.     

Stability and stabilization in switched discrete‐time systems

In this paper, we investigate the stability and stabilization problem for discrete‐time switched systems. We consider a probabilistic case where the system is switched among different subsystems, and the probability of each subsystem being active is defined as its occurrence probability. The relationship between the developed model of the switched system and the Markovian jump system is analyzed. For a switched system with a known subsystem occurrence probabilities, we give a stochastic stability criterion in terms of a linear matrix inequality. Then, we extend the results to a more practical case where the subsystem occurrence probabilities of switching are known to be constant, but their specific values are only known with some uncertainty. A new iterative approach is employed to choose the switching law between the subsystems. For unstable switched systems, mode‐dependent state feedback and static output feedback controllers are developed to achieve the stabilization objective. Finally, several simulation examples are presented to show the efficacy of the proposed criteria and methods. Copyright © 2012 John Wiley & Sons, Ltd.     

A small‐gain approach for adaptive output‐feedback NN control of switched pure‐feedback nonlinear systems

This paper investigates the problem of adaptive output‐feedback neural network (NN) control for a class of switched pure‐feedback uncertain nonlinear systems. A switched observer is first constructed to estimate the unmeasurable states. Next, with the help of an NN to approximate the unknown nonlinear terms, a switched small‐gain technique‐based adaptive output‐feedback NN control scheme is developed by exploiting the backstepping recursive design scheme, input‐to‐state stability analysis, the common Lyapunov function method, and the average dwell time (ADT) method. In the recursive design, the difficulty of constructing an overall Lyapunov function for the switched closed‐loop system is dealt with by decomposing the switched closed‐loop system into two interconnected switched systems and constructing two Lyapunov functions for two interconnected switched systems, respectively. The proposed controllers for individual subsystems guarantee that all signals in the closed‐loop system are semiglobally, uniformly, and ultimately bounded under a class of switching signals with ADT, and finally, two examples illustrate the effectiveness of theoretical results, which include a switched RLC circuit system.     

Quasi‐passivity‐based adaptive stabilization for switched nonlinearly parameterized systems

This paper investigates the adaptive quasi‐passification‐based stabilization problem for a class of switched nonlinearly parameterized systems via average dwell time method. First, when all the subsystems have any same relative degree, the global practical stability is achieved by combining the recursive feedback quasi‐passification design technique with a switched adaptive control technique. The states and parameter estimation errors converge to the ball whose sizes can be reduced by choosing appropriate design parameters. Second, when the system states are unavailable for measurements, adaptive output feedback controllers are designed to stabilize the system using quasi‐passivity. The proposed output feedback controllers do not depend on any state observer. Finally, three examples show the effectiveness of the proposed methods.     

Finite-time asynchronous control of linear time-varying switched systems

In the framework of asynchronous control, finite-time stabilization and finite-time bounded stabilization of linear time-varying (LTV) switched systems are investigated. A necessary and sufficient condition for finite-time stability (FTS) of LTV switched systems is proposed based on differential matrix inequalities (DMIs). Moreover, we extend the FTS result to the case of finite-time boundedness (FTB), and present a sufficient condition of FTB for LTV switched systems using the average dwell time method which can be used for design proposes. Then we turn to the design problem of asynchronously switched control to guarantee FTS or FTB of LTV switched systems and give a sufficient condition for the state feedback stabilization in the form of nonlinear DMIs (NDMIs). A numerical method is proposed to solve NDMIs approximately. Finally, two examples are given to illustrate the validity of the results.     

Luenberger-type cubic observers for state estimation of linear systems

This article introduces a new nonlinear observer for state estimation of linear time invariant systems. The proposed observer contains a (nonlinear) cubic term to enhance observer response. Unlike previously proposed observers, the cubic observer has nonlinear estimation error dynamics. Convergence criteria, performance advantages, and observer-based feedback control with cubic observers are addressed. Simulation examples demonstrating performance improvement compared with linear observers, are included.     

Robust fault detection and adaptive parameter identification for DC-DC converters via switched systems

In this paper, the problem of fault detection and identification for DC-DC converters is presented. First, switched systems model and fault model are analyzed based the switched characteristics of the DC-DC converters, taking the DC-DC buck converter as an example. According to the switched Lyapunov function technique, a fault detection observer and a bank of linear switched fault identification observers are designed for the switched systems. Next, the fault detection observer detects the fault based on the residual produced by the observer output and actual output. After the fault is detected, fault identification observers are activated. The location of fault is identified by comparing the residual evaluation functions. Meanwhile, the adaptive parameter identification is achieved by choosing an appropriate adaptive law. Finally, in order to show the feasibility of the fault detection and identification, the simulation results are given in this article.     

Asynchronous feedback passification for discrete-time switched systems under state-dependent switching with dwell time constraint

This article addresses the passivity analysis and asynchronous feedback passification problems for a class of discrete-time switched systems with dwell time constraint. By exploiting dwell time-dependent storage functions, a state-dependent switching strategy obeying a dwell time constraint is constructed, and the solvability conditions for asynchronous feedback passification are developed in the form of linear matrix inequalities (LMIs). Moreover, the dwell time-dependent asynchronous passive controllers are formulated simultaneously. It has been shown that the derived results are also applicable to the studies of passivity and synchronous feedback passification for discrete-time switched systems under the combined switching strategy. Finally, a three-tank system as a practical example is also provided to illustrate the applicability and effectiveness of our theoretic findings.     

Fault estimation and tolerant control for discrete‐time switched systems with sojourn probabilities

This paper addresses the issue of fault estimation and accommodation for a discrete‐time switched system with actuator faults. Here, we assume that the sojourn probabilities are known a priori. By using the reduced‐order observer method, the sojourn probability approach, and the Lyapunov technique, a fault estimation algorithm is obtained for the considered system. The main objective of this work is to design a dynamic output feedback fault‐tolerant controller based on the obtained fault estimation information such that the closed‐loop discrete‐time switched system with available sojourn probabilities is robustly mean‐square stable and satisfies a prescribed mixed and passivity disturbance attenuation level in the presence of actuator faults. More precisely, a dynamic output feedback fault‐tolerant controller is established in terms of linear matrix inequalities. Finally, numerical examples are provided to illustrate the usefulness and effectiveness of the proposed design technique.