Robust Output Feedback Passification of Linear Systems with Unmodeled Dynamics

For the first time it is proposed and proved that some multi-input multi-output linear systems with unmodeled dynamics can be robustly rendered strictly positive real via static output feedback. In this work, various kinds of unstructured uncertainties are considered, sufficient conditions ensuring robust feedback passification are exploited, and feasible feedback gains are calculated. This new result generalizes existing ones which only deal with exactly modeled systems. It may also play an important role in output feedback variable structure control synthesis. This work is supported partially by the National Natural Science Foundation of China under Grants 60674017 and 60736024.     

Quadratic Stabilization of Uncertain Discrete-Time Switched Systems via Output Feedback

Quadratic stabilization of discrete-time switched systems with norm-bounded time-varying uncertainties is studied. A robust switching rule is proposed to stabilize switched systems by using a designed switched static or dynamic output feedback controller. All the switching rules adopted are constructively designed and state dependent, and they do not rely on any uncertainties.     

基于切换线性系统的DC-DC变换器的输出能控性研究

将DC-DC变换器视为一类混杂动态系统——切换线性系统,尝试在DC-DC变换器控制系统研究中引入切换线性系统的概念,基于系统模型研究DC-DC变换器的输出能控性这一基本控制特性,为各种控制策略在DC-DC变换器中的应用奠定理论基础.研究分为三个部分:(1)引入切换线性系统,并以基本的DC-DC变换器为例,建立变换器的切换线性系统模型;(2)给出切换线性系统输出能控性的定义以及充要条件;(3)分析基本DC-DC变换器的输出能控性,并以Buck变换器为例进行仿真分析和验证验证.本文的研究还表明,分析方法也适应于其它功率变换器,甚至所有开关变换电路的输出能控性研究.     

On the Evaluation of the Exact Output of a Switched Continuous-Time Filter and Applications

In this paper, a study of the operation of switched continuous-time filters (SCTFs), defined as continuous-time filters with elements that are alternatively switched on and off in the signal path, is conducted. A well-known example is the use of switched resistors to multiply their value, but the universe of applications is wider. First, a detailed calculation of the output of an SCTF in the frequency domain, which allows the examination of any SCTF in a general framework, is presented. This result particularly explains the resistor multiplication effect. Three application examples using switched elements are presented and examined as SCTFs: a nonideal sample & hold, a switched active filter that is tuned by varying the duty cycle of the switching, and a switched $G_m$–$C$ filter to implement a chopper amplifier. In all cases, the theoretical background allows the examination of circuit behavior and limitations, and the analysis is supported by measurements or transient simulations.      

Stability Analysis of Switched Positive Systems: A Switched Linear Copositive Lyapunov Function Method

This brief addresses the stability problem of discrete-time switched positive systems. The main contribution lies in two aspects. First, a novel method [the switched linear copositive Lyapunov function (SLCLF)] is proposed to reduce the conservatism of the stability criterion obtained by means of the common linear copositive Lyapunov function. Second, some necessary and sufficient conditions are established for the existence of the switched linear copositive Lyapunov function, assuming that a switched linear positive system is given. A numerical example shows the advantage of the obtained results.      

Stability Analysis of Switched Linear Systems with Uncertainty and Delays

Combining the common quadratic Lyapunov functional approach and free-weighting matrix approach, this paper is devoted to the stability analysis of continuous-time switched linear systems (CTSLS) with uncertainty and time-delays. A particular class of matrix inequalities, the so-called Lyapunov–Metzler inequalities are introduced for the CTSLS to investigate the stability and performance in the presence of the uncertainty and delays. We provide sufficient conditions in terms of the Linear Matrix Inequality criterions to guarantee delay-dependent asymptotically stability under the uncertainty of the CTSLS. The combination of switching rule and switching output feedback controllers which will be designed to stabilize the CTSLS and satisfy a prespecified \({\mathcal{L}}_{2}\) gain performance. A example used jitterbug tools is provided to illustrate the effectiveness of the proposed method.     

事件触发下网络控制系统的动态输出反馈控制

研究了基于事件触发的网络控制系统(NCSs)的动态输出反馈控制(DOFC).通过综合考虑NCSs中的网络诱导延迟和时序错乱的问题,建立了包含事件触发机制和DOFC的闭环模型.与传统的静态控制不同,DOFC可以忽略极点配置受限的问题,增加系统的适应性范围.仿真结果验证了所提出的事件触发机制和DOFC的有效性.     

改进的扰动LPV系统输出反馈预测控制

针对一类带有有界状态干扰的多胞描述LPV系统,文中提出了一种鲁棒预测控制改进方法,并设计了保证系统渐近稳定的输出反馈控制器。为抵消有界状态干扰,该控制器考虑无扰动LPV系统,基于离线状态观测器,采用线性矩阵不等式求解预测控制无穷时域最小-最大优化问题。随后利用离线状态观测器获得扰动LPV系统与无扰动LPV系统状态的估计值之差,以确定保性能的反馈增益,从而得到使扰动LPV系统渐近稳定的最优偏移量,并将其与无扰动系统控制律组合作为最优控制律施加于实际系统。实验结果表明,运用改进的鲁棒预测控制方法能获得较好地控制性能,同时提高了系统的稳定性和解决优化问题的效率,仿真试验也验证了该算法的有效性。     

Passivity Analysis and Passification of Markovian Jump Systems

This paper is concerned with the problems of delay-dependent robust passivity analysis and robust passification for uncertain Markovian jump linear systems (MJLSs) with time-varying delay. The parameter uncertainties are time varying but norm bounded. For the robust passivity problem, the objective is to seek conditions such that the closed-loop system under the state-feedback controller with given gains is passive, irrespective of all admissible parameter uncertainties. For the robust passification problem, desired passification controllers will be designed which guarantee that the closed-loop MJLS is passive. By constructing a proper stochastic Lyapunov–Krasovskii function and employing the free-weighting matrix technique, delay-dependent passivity/passification performance conditions are formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed approaches is demonstrated by a numerical example.     

Finite-Time Stability and Dynamic Output Feedback Stabilization of Stochastic Systems

This paper is concerned with finite-time stability and dynamic output feedback stabilization for Itô type stochastic systems. First of all, it presents a sufficient pth moment finite-time stability criterion of nonlinear stochastic systems. When linear stochastic systems are considered, a finite-time stability condition in the sense of mean square is obtained by choosing a quadratic Lyapunov function. Then, a dynamic output feedback controller is designed to mean-square finite-time stabilize the linear stochastic systems under consideration. Furthermore, the proposed method is extended to finite-time dynamic output feedback control for a class of linear stochastic retarded systems. Numerical examples are finally provided to show the effectiveness of the approach.     

Observer-Based Tracker for Analog Systems with Saturating Actuators and State Constraints Using Digital Redesign and a Weighted Switching Strategy

In this paper, we propose a new dual-rate, observer-based control scheme utilizing digital redesign and a weighted switching strategy for cascaded systems with saturating actuators and state constraints. The weighted switching approach, which uses an evolutionary programming optimal search technique, improves the generally poor transition response caused by nonlinear constraints on saturating actuators and state constraints. An inner loop state compensator is provided to correct the windup effects on the actuator. The designed scheme can easily be implemented using digital processors and enables us to improve the performance of cascaded systems with saturating actuators and state constraints. An illustrative example is presented to demonstrate the effectiveness of the proposed methodology.     

Passivity-based Control for Markovian Jump Systems via Retarded Output Feedback

This paper is concerned with the problem of passivity-based control for Markovian jump systems via retarded output feedback controllers. A delay-dependent passivity criterion is obtained in terms of linear matrix inequalities. Based on this, a sufficient condition is proposed for the design of a retarded output feedback controller which ensures that the closed-loop system is passive. By using the sequential linear programming matrix method, a desired retarded output feedback controller can be constructed. Numerical examples are provided to demonstrate the advantage and effectiveness of the proposed method.     

Output Feedback H ∞ Control for 2-D State-Delayed Systems

In this paper, we consider a class of two-dimensional (2-D) local state-space (LSS) Fornasini–Marchesini (FM) second models with delays in the states, and we study delay-independent and delay-dependent H _∞ control problems via output feedback. First, based on the definition of H _∞ disturbance attenuation γ for 2-D state-delayed systems, we propose a delay-dependent bounded real lemma. Specifically, a new Lyapunov functional candidate is introduced and free-weighting matrices are added to the difference Lyapunov functional for 2-D systems possessing two directions. Then delay-independent and delay-dependent output feedback H _∞ controllers are developed that ensure that the closed-loop system is asymptotically stable and has H _∞ performance γ in terms of linear matrix inequality (LMI) feasibility. Furthermore, the minimum H _∞ norm bound γ is obtained by solving linear objective optimization problems. Numerical examples demonstrate the effectiveness and advantages of the LMI approach to H _∞ control problems for 2-D state-delayed systems. This work was supported in part by the National Natural Science Foundation of China (60525303 and 60604004), NSF of Hebei Province (08M008) and the Key Scientific Research Project of the Education Ministry (204014).     

Passivity and Passification of Uncertain Fuzzy Systems with Impulse

The passivity and feedback passification problems of fuzzy systems with parameter uncertainties and impulse are first presented in this paper. Based on the parallel distributed compensation （PDC） technique, some passivity and passification conditions are proposed in terms of linear matrix inequalities （LMIs）. Numerical examples are given to show the correctness and effectiveness of our theoretical results.     

Gain Scheduled State Feedback Control for Discrete-Time-Varying Polytopic Systems Subject to Input Saturation

In this paper, we study the stability and performance optimization problem of discrete-time-varying polytopic systems with actuator saturation. First, the homogeneous polynomially parameter-dependent matrix function (HPP-DMF for abbreviation) is proposed. Then, a set invariance condition is obtained by applying the HPP-DMF to the Lyapunov function and gain scheduled control law. Based on the set invariance condition, an algorithm is proposed to minimize the worst-case performance. The conditions in the algorithm are expressed in terms of linear matrix inequalities (LMIs). In addition, it is shown that as the degree of the HPP-DMF increases the conditions become less conservative. A numerical example is presented to demonstrate the effectiveness and superiority of the proposed technique.     

Opportunistic Feedback for Multiuser MIMO Systems With Linear Receivers

A novel multiuser scheduling and feedback strategy for the multiple-input multiple-output (MIMO) downlink is proposed in this paper. It achieves multiuser diversity gain without substantial feedback requirements. The proposed strategy uses per-antenna scheduling at the base station, which maps each transmit antenna at the base station (equivalently, a spatial channel) to a user. Each user has a number of receive antennas that is greater than or equal to the number of transmit antennas at the base station. Zero-forcing receivers are deployed by each user to decode the transmitted data streams. In this system, the base station requires users' channel quality on each spatial channel for scheduling. An opportunistic feedback protocol is proposed to reduce the feedback requirements. The proposed protocol uses a contention channel that consists of a fixed number of feedback minislots to convey channel state information. Feedback control parameters including the channel quality threshold and the random access feedback probability are jointly adjusted to maximize the average throughput performance of this system. Multiple receive antennas at the base station are used on the feedback channel to allow decoding multiple feedback messages sent simultaneously by different users. This further reduces the bandwidth of the feedback channel. Iterative search algorithms are proposed to solve the optimization for selection of these parameters under both scenarios that the cumulative distribution functions of users are known or unknown to the base station     

基于切换原理的非均匀采样系统输出反馈控制

在非均匀采样系统中,存在着刷新时间间隔不确定和时变的情况,这给系统控制器的设计造成了很大困难.针对此问题,本文将刷新时间间隔看作时延变量,将不同时延的系统动态变化过程转化为不同子系统的动态变化过程,从而将时延的变化转化为不同子模型之间的切换,最终将非均匀采样系统描述为一类具有有限个子系统的离散时间切换系统.利用输出反馈控制方法,基于平均驻留时间条件,使输出反馈闭环非均匀采样系统指数稳定.最后,通过一个非均匀采样系统仿真实例证明了提出方法的有效性.     

Quantized Output Feedback Control of Uncertain Discrete-Time Systems with Input Saturation

This paper deals with the problem of quantized output feedback control for uncertain discrete-time systems with input saturation. Input quantization case and output quantization case are studied, respectively. The purpose of the study was to design of dynamic output feedback controllers such that all the trajectories of the closed-loop system converge to a small ellipsoid for every initial condition starting from large admissible domain. By solving the optimization problem, the corresponding domains can be obtained. Finally, two simulation examples are provided to demonstrate the applicability of the proposed approach.