WDOP‐based Summation Inequality and its Application to Exponential Stability of Linear Delay Difference Systems

This paper is concerned with the exponential stability analysis of linear delay difference systems. Firstly, a set of weighted discrete orthogonal polynomials (WDOPs) is established by using the Gram‐Schmidt orthogonalization process, and then two WDOPs‐based summation inequalities, including some existing summation inequalities as special cases, are developed. Secondly, these WDOPs‐based summation inequalities are applied to investigate the exponential stability criteria and explicit exponential estimates of solutions of linear delay difference systems. Finally, two numerical examples indicate that the proposed WDOPs‐based approach can derive the exponential stability condition with larger decay rate than the existing ones.     

量子投影滤波

量子滤波器基于贝叶斯原理,利用连续弱测量数据给出当前时刻量子系统状态的最优估计,是量子计算和量子调控技术中极为重要的一环.然而,随着量子系统能级数提高,量子滤波器的实时计算复杂度呈二次型增长.本文介绍了一种量子投影滤波方法,用于减少量子滤波器的实时计算复杂度.基于量子信息几何方法,量子轨迹被限制在了一个由一类非归一化量子密度矩阵组成的子流形中.量子态从而可通过计算子流形的坐标系统来近似获得.仿真实验说明了投影滤波方法的有效性.     

一种改进指数趋近律单向辅助面滑模控制

针对连续非线性系统,结合指数趋近律,采用一种改进指数趋近律的单向辅助面滑模控制方法。首先依据给定的连续非线性系统和状态约束,设计基于指数趋近律的单向辅助面滑模控制器,在此基础上,引入了改进指数趋近律单向辅助面滑模控制器,并给出有限时间收敛的理论证明和收敛时间计算公式。最后通过仿真验证了改进的指数趋近律单向辅助面滑模控制方法具有更快的收敛速度和更有效的抖振抑制能力。     

Guaranteed cost control of switched systems with neutral delay via dynamic output feedback

This article is concerned with the problem of cost-guaranteed dynamic output feedback (DOF) control for a class of continuous-time linear switched system with both discrete and neutral delays. By using the average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed, in terms of a set of linear matrix inequalities (LMIs), to guarantee the exponential stability and a certain bound for the cost function of the closed-loop system, where the decay estimate is explicitly given to quantify the convergence rate. Then, the corresponding solvability conditions for a desired DOF controller under guaranteed cost are established by using the approach of linearising variable transforms. Since these obtained conditions are not all expressed by strict LMIs, the cone complementary linearisation method is exploited to cast them into sequential minimisation problems subject to LMI constraints, which can be easily solved numerically. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.     

Static output feedback control design for linear MIMO systems with actuator dynamics governed by diffusion PDEs

This paper deals with the problem of static output feedback (SOF) control design for a class of diffusion partial differential equation (PDE) and ordinary differential equation (ODE) cascades, where the ODE model is used to describe the dynamics of the multi-input and multi-output (MIMO) plant and the diffusion PDE model is employed to represent the dynamics of actuators. The objective of this paper is to develop a simple as well as effective SOF controller via the Lyapunov's direct method such that the resulting closed-loop system is globally exponentially stable. By constructing a quadratic Lyapunov function, the sufficient condition on the globally exponential stability of the closed-loop cascaded system is presented in terms of linear matrix inequality (LMI). Then, an LMI-based design method of the SOF controller is developed on the basis of the obtained stability analysis result. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method.     

Exponential stability for nonautonomous impulsive neutral partial stochastic evolution equations with delay

In this paper, we give sufficient conditions for the exponential stability of pseudo almost periodic in distribution mild solutions for nonautonomous impulsive neutral partial stochastic evolution equations with delay in a Hilbert space. Our working tools are based on the interpolation theory, the stochastic analysis techniques and fixed point theorem. To illustrate our main result, we study the exponential stability of a pseudo almost periodic in distribution solution for the neutral stochastic model arising in physical systems.     

Stability analysis for networked control systems based on event-time-driven mode

This article studies the problem of stability analysis for a class of networked control systems (NCS), whose control gain is assumed to be known. A switched delay system model is obtained based on the event-time-driven scheme. To solve the stability problem of the new NCS model, a new approach based on the Lyapunov functional exponential estimation method is introduced. By using this method, sufficient conditions are developed to guarantee exponential stability of the considered system. The results obtained may be less conservative than the existing ones from the perspective of maximum allowable transfer interval because the unavailable time is considered in this article. An example is given to show the effectiveness of the proposed method.     

Memoryless H ∞ controller design for switched non-linear systems with mixed time-varying delays

This article deals with the H _∞ control problem for a class of switched non-linear systems with mixed time-varying delays. The novel features here are that the system in consideration is non-linear perturbation with discrete and distributed delays, the time-varying delay is also involved in the observation output, and the controllers to be designed satisfy some exponential stability constraints on the closed-loop poles. By using Lyapunov–Razumikhin functional approach, new sufficient conditions for the H _∞ control with exponential stability constraint are derived in terms of the solution of Riccati-type equations. The approach allows for simultaneous computation of the two bounds that characterise the stability rate of the solution.     

Exponential passivity for output feedback stabilisation of nonlinear uncertain systems

In this article, we address the problem of stabilisation by output feedback for a class of uncertain systems. We consider uncertain systems with a nominal part which is affine in the control and an uncertain part which is norm bounded by a known function. We propose an output feedback such that the closed loop system is globally exponentially stable.     

时变时滞非线性系统的间歇控制

时变时滞广泛存在于各种非线性系统中,研究了时变时滞非线性系统的间歇控制及其在保密通信中的应用问题,提出了一种间歇控制策略,理论上分析了其正确性,并且给出一个定理来确定控制器的相关参数。根据提出的定理,设计出间歇控制器使得两个含有时变时滞的Chua电路指数达到同步。将该方法应用到混沌保密通信中,在两个系统达到同步的基础上,发送端的信号能够在接收端很好地恢复出来,表明了该方法的可行性。