Sensor allocation with guaranteed exponential stability for linear multi‐rate sampled‐data systems

This paper addresses sensor allocation with guaranteed exponential stability for linear multi‐rate sampled‐data systems. It is assumed that a continuous‐time linear plant is exponentially stabilized by a continuous‐time linear controller. Given sensors with incommensurate sampling rates, the objective is to allocate each state to a sensor such that the resulting multi‐rate sampled‐data system remains exponentially stable. The main contributions of this paper are twofold. First, we propose sufficient Krasovskii‐based conditions to partition the state vector among sensors such that exponential stability of the closed‐loop system is guaranteed. Second, the problem of finding a partition that guarantees exponential stability is cast as a mixed integer program subject to linear matrix inequalities. The theoretical results are successfully applied to two robotic problems: path‐following in unicycles and hovering in quadrotors. Copyright © 2015 John Wiley & Sons, Ltd.     

Sufficient conditions for stability and stabilization of networked control systems with uncertainties and nonlinearities

In this paper, we consider the problem of robust stability and stabilization for networked control systems (NCS) with uncertain/nonlinear dynamics AUTHOR: Please check that authors and their affiliations are correct. in which the network‐induced delays are time‐varying and bounded. Based on some recent achievements, a relatively simple Lyapunov–Krasovskii functional is proposed to derive sufficient conditions both for analysis and synthesis of NCS in the form of LMIs depending on the delay bounds. The effectiveness of the proposed method is illustrated by several benchmark examples available in the literature. Copyright © 2014 John Wiley & Sons, Ltd.     

Necessary exponential stability conditions for linear periodic time‐delay systems

Exponential stability necessary conditions for linear periodic time‐delay systems are presented. They are obtained with the help of new properties of the Lyapunov matrix in the framework of Lyapunov–Krasvoskii functionals of complete type. An academic example illustrates our results. Copyright © 2016 John Wiley & Sons, Ltd.     

离散线性切换系统的一致有限时间稳定分析和反馈控制及其在网络控制系统中的应用

研究了一类离散线性切换系统的一致有限时间稳定性分析和反馈镇定．基于线性矩阵不等式技术,给出了在任意切换信号作用下,离散线性切换系统有限时间稳定和有限时间有界的充分条件,并给出了离散线性切换控制系统一致有限时间状态反馈控制器的设计方法．将上述分析结果应用于一类丢包有界的网络控制系统,得到了保证其有限时间稳定的反馈控制器．最后,通过两个数值仿真例子验证了所提方法的有效性．     

A separation method of transmission delays and data packet dropouts from a lumped input delay in the stability problem of networked control systems

This paper proposes a separation method of a transmission delay and data packet dropouts from a lumped input delay in the stability problem of a networked control system, where both the transmission delay and the data packet dropouts are involved. By modeling data packet dropouts as sampling processes and the transmission delay as a state delay, the networked control system is represented as a sampled‐data system with aperiodic sampling and a state delay. In order to separate the state delay and the sampling, the sampled‐data system is transformed into a new system with an integral operator, where the sampling is embedded into the integral operator. By investigating the integral operator's gain and passivity, a novel Lyapunov functional is constructed to address the stability problem. The obtained stability results are dependent on both the data packet dropouts and the time delay. A numerical example is provided to demonstrate that the stability results are less conservative than some existing ones. Copyright © 2016 John Wiley & Sons, Ltd.     

MIMO网络控制系统的建模与分析

针对网络只存在于传感器节点与控制器节点之间的多输入多输出(MIMO)网络控制系统,研究了系统建模和稳定性问题.设传感器节点和控制器节点均为时间驱动,且它们的采样存在着固定的时间差,网络诱导时延的上界大于一个采样周期,建立了此类网络控制系统的模型.基于Lyapunov函数和线性矩阵不等式(LMIs)方法,给出了闭环系统渐近稳定的充分条件.仿真表明本文的方法是有效的.     

New insight into delay‐dependent stability of time‐delay systems

This paper presents a new insight into the delay‐dependent stability for time‐delay systems. Because of the key observation that the positive definiteness of a chosen Lyapunov–Krasovskii functional does not necessarily require all the involved symmetric matrices in the Lyapunov–Krasovskii functional to be positive definite, an improved delay‐dependent asymptotic stability condition is presented in terms of a set of LMIs. This fact has been overlooked in the development of previous stability results. The importance of the present method is that a vast number of existing delay‐dependent results on analysis and synthesis of time‐delay systems derived by the Lyapunov–Krasovskii stability theorem can be improved by using this observation without introducing additional variables. The reduction of conservatism of the proposed result is both theoretically and numerically demonstrated. It is believed that the proposed method provides a new direction to improve delay‐dependent results on time‐delay systems. Copyright © 2013 John Wiley & Sons, Ltd.     

时延丢包网络控制系统的分析与控制

针对网络控制系统中同时存在时延和丢包问题,基于零阶保持器的工作机制,将同时受时延和丢包影响的网络控制系统建模为输入带有时延的控制系统,根据李雅普诺夫稳定性理论和时滞系统理论得出控制系统的时滞相关稳定性条件,进一步基于锥补线性化的方法给出控制器的设计方法,有效解决了网络控制系统中同时存在时延和丢包的控制问题。仿真算例表明所提方法的有效性。     

LMI characterization of the strong delay-independent stability of linear delay systems via quadratic Lyapunov–Krasovskii functionals

In this note is proposed an analogue for linear delay systems of the characterization of asymptotic stability of the rational systems by the solvability of associated Lyapunov equation. It is shown that strong delay-independent stability of delay system is equivalent to the feasibility of certain linear matrix inequality (LMI), related to quadratic Lyapunov–Krasovskii functionals.     

Robust stability of nonlinear time‐delay systems with interval time‐varying delay

This paper deals with the problem of obtaining delay‐dependent stability conditions and L₂‐gain analysis for a class of nonlinear time‐delay systems with norm‐bounded and possibly time‐varying uncertainties. No restrictions on the derivative of the time‐varying delay are imposed, though lower and upper bounds of the delay interval are assumed to be known. A Lyapunov–Krasovskii functional approach is proposed to derive novel delay‐dependent stability conditions which are expressed in terms of linear matrix inequalities (LMIs). To reduce conservatism, the work exploits the idea of splitting the delay interval in multiple regions, so that specific conditions can be imposed to a unique functional in the different regions. This improves the computed bounds for certain delay‐dependent integral terms, providing less conservative LMI conditions. Examples are provided to demonstrate the reduced conservatism with respect to the available results in the literature. Copyright © 2010 John Wiley & Sons, Ltd.     

不确定时延网络控制系统的保性能控制

在工程实际网络控制系统中,不仅要求系统能够保持稳定,还要系统具有一定的性能指标,采用状态反馈控制是一种非常有效的控制方式。针对一类线性不确定时延网络控制系统,研究了在有记忆状态反馈控制器下的保性能控制问题。利用Lyapunov函数和线性矩阵不等式的方法,给出了网络控制系统保性能控制律存在的条件和相应的状态反馈控制器的设计方法。最后,通过Matlab数值仿真算例验证了该方法的有效性和正确性。     

Less conservative stability criteria for linear systems with interval time‐varying delays

The problem of the stability of a linear system with an interval time‐varying delay is investigated. A new Lyapunov–Krasovskii functional that fully uses information about the lower bound of the time‐varying delay is constructed to derive new stability criteria. It is proved that the proposed Lyapunov–Krasovskii functional can lead to less conservative results than some existing ones. Based on the proposed Lyapunov–Krasovskii functional, two stability conditions are developed using two different methods to estimate Lyapunov–Krasovskii functional's derivative. Two numerical examples are given to illustrate that the two stability conditions are complementary and yield a larger maximum upper bound of the time‐varying delay than some existing results. Copyright © 2013 John Wiley & Sons, Ltd.     

On exponential stability of integral delay systems

This paper is concerned with exponential stability of a class of integral delay systems with a prescribed decay rate. First, by carefully exploring the literature on this topic, a delay decomposition approach is established to reduce the conservatism in the existing sufficient conditions by constructing new Lyapunov–Krasovskii (LK) functionals. It is proven that the proposed sufficient conditions are less conservative than a recently established set of sufficient conditions. Second, by analyzing the characteristic equation of the considered integral delay system, necessary and sufficient conditions for the stability are obtained by computing the right-most zeros of a certain auxiliary point-delay linear system, for which stability criteria that are easy to test are also established based on this method. Numerical examples illustrate the effectiveness of the obtained results.     

Necessary conditions for the exponential stability of time‐delay systems via the Lyapunov delay matrix

Exponential necessary stability conditions for linear systems with multiple delays are presented. The originality of these conditions is that, in analogy with the case of delay free systems, they depend on the Lyapunov matrix function of the delay system. They are validated by examples for which the analytic characterization of the stability region is known. Copyright © 2013 John Wiley & Sons, Ltd.     

Model predictive control for networked control systems

This paper investigates the problem of model predictive control for a class of networked control systems. Both sensor‐to‐controller and controller‐to‐actuator delays are considered and described by Markovian chains. The resulting closed‐loop systems are written as jump linear systems with two modes. The control scheme is characterized as a constrained delay‐dependent optimization problem of the worst‐case quadratic cost over an infinite horizon at each sampling instant. A linear matrix inequality approach for the controller synthesis is developed. It is shown that the proposed state feedback model predictive controller guarantees the stochastic stability of the closed‐loop system. Copyright © 2008 John Wiley & Sons, Ltd.     

A stability criterion for asynchronously switched linear systems via sampled‐data control

This paper considers an asynchronous problem for sampled‐data control of switched linear systems, which are described as switched linear systems with an input delay. To handle the problem, this paper proposes a stability criterion for the systems by constructing a novel Lyapunov‐Krasovskii functional dependent not on system modes but on controller modes. The functional continuously remains when the system modes are switched but discontinuously changes whenever the controller mode moves to the current system mode at the sampling instants. Furthermore, the functional is allowed to increase or decrease up to a certain level when the functional discontinuously changes and to increase up to a certain level when the system modes and the controller modes are asynchronous. Based on the functional, this paper derives an average dwell time associated with the interval of samplings and the incremental level of the functional for guaranteeing the stability of the systems. A numerical example illustrates the validation of the proposed method.     

Sampled‐data control of nonlinear networked systems with time‐delay and quantization

In this paper, the stabilization problem of a class of nonlinear networked systems with time‐delay and quantization through sampled‐data control is investigated. With sampled‐data control, sufficient conditions to guarantee the trivial solution of the nonlinear networked system to be asymptotically stable without any quantization or with uniform quantization are derived. Finally, an example of a continuous‐time nonlinear system controlled through a digital controller and a communication channel is given to illustrate the effectiveness of the proposed control methods. Copyright © 2015 John Wiley & Sons, Ltd.     

网络化控制系统的信息调度与稳定性研究

针对具有通信约束的变速率网络化控制系统模型，研究在有系统信息丢失的情形下闭环系统的渐近稳定性问题；同时针对框架化的信息调度方法，探讨了在给定网络变速率采样模式下，通过设计动态反馈控制律保持闭环系统渐近稳定的方法来评判信息调度方法的适定性。     

Lyapunov–Krasovskii functionals and frequency domain: delay‐independent absolute stability criteria for delay systems

The present paper is devoted to the study of absolute stability of delay systems with nonlinearities subject to sector conditions. We construct quadratic candidate Lyapunov–Krasovskii functional, whose decreasingness along trajectories is expressed in terms of linear matrix inequalities. We then show that the feasibility of the latter implies some frequency‐domain conditions, which may be seen as delay‐independent versions of the circle criterion and the Popov criterion. Copyright © 2001 John Wiley & Sons, Ltd.