Event-Triggered L1-Gain Control of Nonlinear Positive Switched Systems

This paper is concerned with the event-triggered L_1-gain control of a class of nonlinear positive switched systems. First, an event-triggering condition in the form of 1-norm is presented for the systems. By virtue of the event-triggering strategy, the original system is transformed into an interval uncertain system. An event-triggered L_1-gain controller is designed by decomposing the controller gain matrix into the sum of nonnegative and non-positive components. Under the design controller, the resulting closed-loop systems are positive and L_1-gain stable. The obtained approach is developed for the systems subject to input saturation. All presented conditions are solvable in terms of linear programming. Finally, two examples are provided to verify the effectiveness of the design.     

Exponential stability of linear distributed parameter switched systems with time-delay

In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems (DPSS) in Hilbert space. For a given family of exponential stable subsystems, this paper focuses on finding conditions to guarantee the overall DPSS’ exponential stability. Based on semigroup theory, by applying piecewise Lyapunov-Krasovskii functionals method incorporated average dwell time approach, sufficient conditions for exponential stability are derived. These conditions are given in the form of linear operator inequalities (LOIs) where the decision variables are operators in Hilbert space, and the stability properties depend on switching rule. Being applied to heat switched propagation equations, these LOIs are reduced to standard Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed result.     

Robust exponential stability of switched interval interconnected systems with unbounded delay

In this paper, a class of switched interval interconnected systems with unbounded delay were investigated. On the assumption that the interconnected functions of the systems satisfied the global Lipschitz condition, by using vector Lyapunov methods and M-matrix theory, the integrodifferential inequalities with unbounded delay were constructed. By the stability analysis of the integrodifferential inequalities, the sufficient conditions to ensure the robust exponential stability of the interval interconnected systems were obtained. By using average dwell time approach, conditions for guaranteeing the robust exponential stability of the switched delay interval interconnected systems were derived. Finally, two numerical examples were given to illustrate the correction and effectiveness of the proposed theory.     

Exponential passive filtering for a class of nonlinear jump systems

The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlinearities satisfy the quadratic condition. Based on the passive filtering theory, the sufficient condition for the existence of the mode-dependent passive filter is given by analyzing the reconstructed observer system. By using the appropriate Lyapunov-Krasovskii function and applying linear matrix inequalities, the design scheme of the passive filter is derived and described as an optimization one. The presented exponential passive filter makes the error dynamic systems exponentially stochastically stable for all the admissible uncertainties, time-delays and nonlinearities, has the better abilities of state tracking and satisfies the given passive norm index. Simulation results demonstrate the validity of the proposed approach.     

Admissibility analysis and control synthesis for switched linear singular systems

The problem of admissibility analysis and control synthesis of discrete-time switched linear singular (SLS) systems for arbitrary switching laws is solved. By using the switched Lyapunov function approach, some new sufficient conditions under which the SLS system is admissible for arbitrary switching laws are derived in terms of linear matrix inequalities (LMIs). Based on the admissibility results, control synthesis is then to design switched state feedback and static output feedback controllers, guaranteeing that the resulting closed-loop system is admissible. The presented results can be viewed as the extensions of previous works on switched Lyapunov function approach from the regular switched systems to singular switched cases. Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions.     

Delay-dependent exponential stability of impulsive stochastic systems with time-varying delay

The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay.Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors,few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems.Firstly,the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem.Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities.In particular,the estimate of the exponential convergence rate is also provided,which depends on system parameters and impulsive effects.The obtained results show that the system will stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous flows,and impulses may be used as controllers to stabilize the underlying stochastic system.Numerical examples are given to show the effectiveness of the results.     

有包丢失的动态输出反馈奇异网络化系统稳定性分析

基于正则、无脉冲的奇异被控对象,研究了同时具有时延和数据包丢失的动态输出反馈网络控制系统的建模和稳定性问题。 当时延不大于一个采样周期、数据包丢失率一定时,将动态输出反馈网络控制系统建模为数据包丢失率约束的异步动态切换系统,利用切换系统和线性矩阵不等式方法,推导出数据包丢失率约束的系统指数稳定的充分条件,并且给出了系统指数稳定的指数衰减率以及最大容许数据包丢失率。仿真实验说明分析方法和研究结果是有效可行的。     

线性不确定随机系统时滞相关的H∞滤波

研究了一类带有时变状态时滞和参数不确定性的连续时间线性随机系统的鲁棒H_∞滤波问题。目的是设计一个线性滤波器使滤波误差动态系统是指数均方稳定的,并满足给定的H_∞性能指标。应用描述符系统模型转换,建立了新的Lyapunov-Krasovskii 函数。通过引入自由加权矩阵,消除了Lyapunov矩阵和系统矩阵的乘积项,从而无需在滤波器设计过程中对Lyapunov矩阵作任何约束,这在很大程度上降低了滤波器设计的保守性。基于LMI方法,针对精确已知随机系统和带有结构不确定性的随机系统,分别提出了时滞相关的鲁棒H_∞滤波器存在的充分性条件。仿真结果表明所提出的设计方法是有效的。     

Packet-loss-dependent stabilization of NCSs with network-induced delay and packet dropout

This paper is concerned with controller design of networked control systems (NCSs) with both network-induced delay and arbitrary packet dropout.By using a packet-loss-dependent Lyapunov function,suffic...     

时滞切换系统指数稳定性分析：Lyapunov-Krasovskii泛函方法

考虑由两个线性时滞子系统构成的切换系统,分析其在任意切换序列作用下保持指数稳定性的条件.分别利用二次型与逐段二次型的Lyapunov-Krasovskii泛函构造方式给出了以线性矩阵不等式所表述的稳定性判据;进而通过状态变量代换结合积分不等式技巧证明了指数衰减率对于所有切换序列一致成立,即其完全取决于系统的结构特征.最后给出了一个算例.     

一类非线性切换系统的稳定性分析

主要研究了一类非线性切换系统在某种切换律下的稳定性。证明了如果所有的子系统是线性时变的,并且在系统的Cauchy矩阵的范数满足某种条件的情况下,整个切换系统在任意切换律下是全局指数稳定的。研究了其带非线性扰动项的系统,在适当的假设下,建立了这种系统的全局稳定性特性。研究了某些子系统不满足上述Cauchy矩阵的范数条件的切换系统在某种切换律下的稳定性特性。     

Event-Triggered Consensus for Discrete-Time Multi-agent Systems with Parameter Uncertainties Based on a Predictive Control Scheme

In this paper, the event-triggered consensus for linear discrete-time multi-agent systems with parameter uncertainties is investigated. The parameter uncertainty is assumed to be normbounded. An event-triggered consensus protocol based on the predictive control method is proposed to make the multi-agent system achieve consensus. And for the design of the consensus protocol, the problem of estimating the control input is transformed into the problem of estimating state differences between agents. Furthermore, the event-triggered consensus protocol proposed in this paper only demands each agent to mornitor its state to determine its event-triggered instants. A sufficient existence condition for the consensus protocol is proposed based on the linear matrix inequality. And a sufficient condition for the nonexistence of the Zeno-like behaviour is also derived. Finally, a numerical example is given to illustrate that the event-triggered consensus protocol proposed in this paper can make the multi-agent system with parameter uncertainties achieve consensus effectively.     

Approximating the Spectral Abscissa for Switched Linear Systems via Coordinate Transformations

In this paper,an approach of square coordinate transformation is proposed to approximate the spectral abscissa for continuous-time switched linear systems.By applying elementary transformations iteratively,a series of minimums of least μ1 matrix set measures are obtained,which are utilized to approximate the spectral abscissa of the switched system.The approach is developed into tractable numerical algorithms that provide upper bound estimates of the spectral abscissa.Numerical simulations show the effectiveness of the proposed method.     

Performance Improvement of NCSs Under Complex Network via Concurrent Paths

Different from the single paths between controllers and plants of networked control systems(NCSs), the complex network provides widespread links and brings plenty of paths from the controller side to the plant side. Benefit from this advantage, a novel data transmission dispatching strategy is proposed. When the direct path can not satisfy the condition of system demand, neither stability nor performance, some specified paths compose a concurrent-path to transmit the control signal concurrently. Firstly, the networked control systems(NCSs) are expressed by the switched systems model with the constant network-induced delay, and the network communication is described as a packet-loss process. Secondly, taking system's exponential decay rate as its performance indicator, the relationship between control signal transmission paths and system performance is quantitatively given by considering packet losses as the compound poisson process and the alternating renewal process. Then, due to that different combination of paths induces the different statistical properties of packet losses, the approach to find an appropriate concurrent-path is proposed concerning two mutually constrained factors, the system performance demand and the utilization of network resources. After the theoretical analysis, a distributed communication platform based on peer-to-peer(P2P) network technology is designed and implemented to realize the concurrent-path transmission on internet. Finally, the practical experiment on the platform demonstrates the validity and effectiveness of proposed approach.     

增益调度积分型切换项滑模控制器设计

针对一类不确定离散系统,提出了一种增益调度积分型滑模控制器,并分析其鲁棒H_∞性能。首先,通过状态扩维,得到含有输出误差积分项的离散模型,并利用理想滑模运动性质得出滑模等效控制律,利用输出误差积分项设计增益调度滑模补偿控制律。然后,将滑模闭环控制系统等效为切换系统,基于切换系统相关理论推导了滑模控制参数与闭环控制系统的二次稳定性、鲁棒H_∞性能指标的关系。最后,通过对不确定项和非线性项的处理得到线性矩阵不等式(linear matrix inequality, LMI),再求解该不等式,得出满足控制性能要求的滑模控制参数。仿真实验中分析了控制算法的暂态性能和扰动抑制能力,证明了该方法的有效性。     

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.     

基于观测器的一类不确定非线性系统自适应输出反馈控制

针对一类不确定非线性系统,基于非线性状态观测器采用回馈递推(Backstepping)设计方法提出了一种鲁棒自适应L2增益控制方案。该控制方案首先对系统的不可观测状态设计非线性状态观测器,在此基础上通过多步递推得到系统的控制律并设计了未知干扰的参数自适应律,使系统具有L2增益性能。同时把采用常规设计方法需要对过多参数进行辨识问题简化为只需对与未知干扰个数相同的参数进行辨识的问题,简化了控制器结构。最后通过仿真算例验证了所设计控制方案的有效性。     

基于粒子群算法的开关系统最优控制问题的数值算法

针对开关系统,给出了数学模型并引出了其最优控制问题,提出开关系统最优控制问题的加权粒子群算法,给出了相关的推理过程及算法步骤。加权粒子群算法不必找出支付泛函关于时间的显式表达,就可以找到其最优解,同样适用于其子系统为非线性的情形。分析了粒子群算法快速全局优化的特点,说明该算法能找到优化问题的全局最优解。以开关动态系统和一般开关线性二次问题的数值算例验证了该方法的有效性。     

Robust Stabilization of Non-minimum Phase Switched Nonlinear Systems with Uncertainty

This paper investigates the problem of robust stabilization of a class of switched nonlinear system with uncertain dynamics where each subsystem represents a non-minimum phase. The authors first construct a stabilizing sliding mode controller for each subsystem to stabilize individually its own unstable internal dynamics. Then, a switching strategy is introduced to select the most appropriate diffeomorphism through an infinity of diffeomorphisms. Sufficient conditions are specifically given for the exponential stability and the exponential upper bound of the trajectory of the switched subsystem,which guarantees the global asymptotical stability of the resulting switched system. Obviously, the proposed control approach can improvemore the transient state, compared to a feedback linearization based on only one diffeomorphism. Simulation studies illustrate the effectiveness of the suggested approach.     

Stability Analysis of Event-Triggered Networked Control Systems with Time-Varying Delay and Packet Loss

Networked control systems(NCSs) are facing a great challenge from the limitation of network communication resources. Event-triggered control(ETC) is often used to reduce the amount of communication while still keeping a satisfactory performance of the system, by transmitting the measurements only when an event-triggered condition is satisfied. However, some network-induced problems would happen inevitably, such as communication delay and packet loss, which can degrade the control performance significantly and can even lead to instability. In this paper, a periodic eventtriggered NCS considering both time-varying delay and packet loss is studied. The system is discretized into a piecewise linear system with uncertainty. Then the model is handled by a polytopic overapproximation method to be more suitable for stability analysis. Finally, stability conditions are obtained and presented in terms of linear matrix inequalities(LMIs). The result is illustrated by a numerical example.