Infinite Markov jump-bounded real lemma

A bounded real lemma is established, providing an equivalent condition to stochastic stability (SS) of a continuous-time infinite Markovian jump linear system (MJLS) with a prescribed L₂-stochastic disturbance attenuation level γ in terms of existence of solutions to an infinite set of coupled linear matrix inequalities (LMIs). Besides the interest in its own right, the main result provides a fundamental tool for the development of an H_∞-like theory devoted to this class of systems.     

A general method for function synthesis†

This paper proposes some mathematical relations that may be used to describe conditions in systems after connections have been altered. The common rules of conservation of charge and flux emerge as particular instances of these more general relations. The results obtained apply in systems containing amplifiers (subject to model adequacy)—a case excluded by the normal conservation stipulations.

The conditions under which a peculiar form of instability is encountered are presented.     

Control synthesis via state feedback with finite frequency specifications for time-delay systems

This article considers the problem of control synthesis via state feedback for linear time-delay systems with design specifications in finite frequency ranges. First, a finite frequency performance analysis condition for time-delay systems is presented. Then, a resulting state feedback control synthesis condition is given in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, the design procedure and the effectiveness of the proposed method are illustrated via a numerical design example.     

Active fault tolerant control for a class of linear time-delay systems in finite frequency domain

This article deals with the problem of active fault tolerant control (AFTC) for a class of linear time-delay systems in a finite frequency domain. A new ?_∞ controller in generalised internal model control architecture with an observer-based fault estimator is proposed for the AFTC system. Based on online fault estimation and accommodation, the closed-loop system stability and ?_∞ performance for both fault free and faulty cases are guaranteed. With the aid of the generalised Kalman–Yakubovich–Popov lemma for time-delay systems, sufficient conditions on the existence of such an AFTC system ensuring simultaneous finite frequency estimation and control performance are derived. The calculation procedure of the parameter matrices of the fault estimator and ?_∞ controller is also proposed. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Indirect adaptive fuzzy and impulsive control of nonlinear systems

The problem of indirect adaptive fuzzy and impulsive control for a class of nonlinear systems is investigated. Based on the approximation capability of fuzzy systems, a novel adaptive fuzzy and impulsive control strategy with supervisory controller is developed. With the help of a supervisory controller, global stability of the resulting closed-loop system is established in the sense that all signals involved are uniformly bounded. Furthermore, the adaptive compensation term of the upper bound function of the sum of residual and approximation error is adopted to reduce the effects of modeling error. By the generalized Barbalat's lemma, the tracking error between the output of the system and the reference signal is proved to be convergent to zero asymptotically. Simulation results illustrate the effectiveness of the proposed approach.     

含对数项分数阶T混沌系统的滑模同步

利用Barbalat引理、分数阶稳定性理论,通过构造合适的分数阶线性滑模面和分数阶比例积分滑模面,设计合理的控制器,实现整数阶、分数阶T混沌系统滑模同步控制。研究结果表明:一定条件下,分数阶T混沌系统的驱动-响应系统能够达到滑模同步,用Matlab数值仿真验证了结论的正确性。     

Specialized fast algorithms for IQC feasibility and optimization problems

The conventional way to treat integral quadratic constraint (IQC) problems is to transform them into semi-definite programs (SDPs). SDPs can then be solved using interior point methods which have been proven efficient. This approach, however, is not always the most efficient since it introduces additional decision variables to the SDP, and the additional decision variables sometimes largely increase the complexity of the problem. In this paper, we demonstrate how to solve IQC problems by other alternatives. More specifically, we consider two cutting plane algorithms. We will show that in certain cases these cutting plane algorithms can solve IQC problems much faster than the conventional approach. Numerical examples, as well as some explanations from the point of view of computational complexity, are provided to support our point.     

多时变时滞系统的鲁棒稳定及有界实引理的时滞相关条件

对于多时变时滞系统,引入表示牛顿-莱布尼兹公式中各项的相互关系的自由权矩阵,获得了基于线性矩阵不等式(LMI)描述的系统鲁棒稳定的时滞相关条件,并说明了时滞相关条件和时滞无关条件的相互关系.在此基础上,将其推广到有界实引理的时滞相关条件.所得结果克服了已有结果的保守性.最后给出实例说明本文方法的有效性.     

On necessity proof of strict bounded real lemma for generalized linear systems with finite discrete jumps

Some preliminary results on strict bounded real lemma for tame-varying continuous linear systems are proposed,where uncertainty in initial conditions, terminal cost and extreme of the cost fimction are dealt with explicidy. Based on these results, a new recursive approach is proposed in the necessity proof of strict bounded real lemma for generalized linear system with finite discrete jumps.     

关于φK-偏差函数的一类上界的最佳情形

研究了拟共形理论中著名的Hübner不等式中的函数M（r）=2/π（r′）2κ（r）κ′（r）＋log r的形如（r′）α·log 4的上界估计中的最佳指数α为何值这一问题,获得了max{c：不等式M（r）〈（r′）c log4对一切r∈（0,1）成立}的上下界估值,证明了min{c：M（r）〉（1-r）c log4一切r∈（0,1）成立}=1。从而改进了已知的此类估计与由此类估计得出的拟共形理论中极为重要的Hersch-Pfluger偏差函数φK（r）的上界以及相应的显式拟共形Schwarz引理。