A new result on stability analysis for stochastic neutral systems

This paper discusses the mean-square exponential stability of stochastic linear systems of neutral type. Applying the Lyapunov–Krasovskii theory, a linear matrix inequality-based delay-dependent stability condition is presented. The use of model transformations, cross-term bounding techniques or additional matrix variables is all avoided, thus the method leads to a simple criterion and shows less conservatism. The new result is derived based on the generalized Finsler lemma (GFL). GFL reduces to the standard Finsler lemma in the absence of stochastic perturbations, and it can be used in the analysis and synthesis of stochastic delay systems. Moreover, GFL is also employed to obtain stability criteria for a class of stochastic neutral systems which have different discrete and neutral delays. Numerical examples including a comparison with some recent results in the literature are provided to show the effectiveness of the new results.     

An integral-equation function-space method for solving inequality-constrained optimal control problems†

A function-space method using an integral equation representation of the second variation is applied to inequality-constrained optimal control problems. Numerical solutions for a bang-bang control problem and a singular control problem are solved using the computational algorithm.     

Interval frequency negative imaginary systems

This paper studies interval frequency negative imaginary (IFNI) systems based on minimal state-space realisations. Firstly, the concept of the IFNI transfer functions is introduced, and the relationship between the IFNI transfer functions and the interval frequency positive real transfer functions is established. Secondly, based on the generalised KYP lemma, a necessary and sufficient condition is derived for IFNI transfer functions with minimal state-space realisation in terms of linear matrix inequalities. Our results coincide with the existing negative imaginary lemma when the interval frequency set becomes the positive frequency set. Also, a time domain interpretation of the IFNI property is provided in terms of the system input, output and state. Finally, two examples are used to illustrate the developed theory.     

时变时滞随机非线性系统的自适应神经网络跟踪控制

针对一类具有时变时滞的不确定随机非线性严格反馈系统的自适应跟踪问题,利用Razumikhin引理和backstepping方法,提出一种新的自适应神经网络跟踪控制器.该控制器可保证闭环系统的所有误差变量皆四阶矩半全局一致最终有界,并且跟踪误差可以稳定在原点附近的邻域内.仿真例子表明所提出控制方案的有效性.     

基于广义KYP 引理方法的奇异摄动系统有限频段正实性能分析

基于广义KYP引理,研究了奇异摄动系统的有限频段正实性能.根据奇异摄动系统的双频标特性,即有低频和高频两种频域尺度,应用广义KYP引理,分别研究了奇异摄动系统的降阶子系统在其低频段和高频段的正实性,并以线性矩阵不等式形式给出了上述子系统在有限频段正实的充分必要条件.在此基础上,进一步证明了奇异摄动系统在一定条件下是部分频段正实的.     

Schwarz引理在非凸域上的推广

利用一特殊双全纯映射,将经典的单位圆上的Schwarz引理进行推广,得出了一类特殊非凸域-Hartogs三角形上集合形式的Schwarz引理.     

Improved leaderless consenus criteria of networked multi-agent systems based on the sampled data

This paper is concerned with leaderless consensus of networked multi-agent systems with Lipschitz-type nonlinear dynamics based on the sampled data. By introducing a weighted average state of all nodes as the virtual leader, the error variables are defined as the distance between agents and the virtual leader. The improvements are done in two directions. First, several consensus conditions are derived by linear matrix inequalities based on Finsler's lemma instead of algebraic criteria based on the general algebraic connectivity. Finsler's lemma is utilised to deal with the linear dependence of the error variables. Second, a distributed event-triggered transmission strategy under the periodic sampling scheme is proposed to reduce the communication between agents and the control updates, which only need to check the event condition at each sampling instant, avoiding the continuous monitor. With the improved strategies, one theorem and two corollaries are derived and a co-design approach of the feedback gain and the event-triggered matrix is also presented. Finally, an example is provided to validate the effectiveness of the theoretical results.