On Detectability and Observability of Discrete‐Time Stochastic Markov Jump Systems with State‐Dependent Noise

This paper mainly studies the notions of detectability and observability for discrete‐time stochastic Markov jump systems with state‐dependent noise. Two concepts, called “W‐detectability” and “W‐observability,” for such systems are introduced, and are shown to coincide with the other concepts on detectability and observability reported recently in literature. Moreover, some criteria and interesting properties for both W‐detectability and W‐observability are obtained.     

New results in 2D optimal control theory

The infinite horizon optimal control problem is solved for 2D systems described by the Fornasini-Marchesini model. An ₂-approach permits us to reduce the optimal control problem to a norm minimization one in Hilbert spaces. Both necessary and sufficient conditions for solvability and the structure of the solution are established. Moreover, a comparison with known results is presented, and the singularities of the 2D Riccati equation are examined in order to characterize suboptimal control laws that apply whenever the solvability conditions are not satisfied.     

卷积积分和拉普拉斯变换在一阶电路中的应用

电路的任意激励的零状态响应,可以用卷积积分和拉普拉斯交换的方法求解。本文通过两个一阶电路的实例,阐述了两种方法的应用特点。     

Sensors structures and regional detectability of parabolic distributed systems

In this paper, we deal with the linear infinite dimensional systems in a Hilbert space where the dynamics of the system is governed by strongly continuous semi-groups. We study the concept of asymptotic (exponential) regional detectability in connection with the structures of sensors for a class of parabolic distributed parameter systems. For different sensors structures, we give the characterization of the asymptotic (exponential) regional detectability in order that asymptotic (exponential) regional observability be achieved. Furthermore, we apply these results to the regional observer for distributed parameter diffusion systems.     

Robust estimation of continuous nonlinear plants with discrete measurements

In this work the problem of designing a state estimator for completely or partially observable continuous nonlinear plants with discrete measurements is addressed. The combination of a geometric approach with a stability analysis yields an estimator design methodology with a nonlinear detectability condition susceptible of testing, a systematic estimator construction, a robust convergence criterion coupled with a simple tuning scheme, as well as a rationale to explain the interplay between sampling time, estimator gains, and estimator functioning. Comparing with the continuous measurement case where the convergence is attained by tuning the gain above a low limit, in the discrete measurement case the loss of information due to the measurement sampling increases the size of the lower gain limit, and imposes sampling time and high gain limits. The proposed methodology is applied to address the estimation problem of a class of solution homopolymerization reactors, and is tested with a methyl-methacrylate polymerization run taken from a previous extended Kalman filter implementation study with experimental data.     

离散事件系统的可测性

讨论基于自动机/形式语言模型的离散事件系统（DES）的可测性问题。可测性即为根据系统的可观事件和状态输出的信息估计系统的当前状态。定义了四种可测性：强可测性,弱可测性,强周期可测性,弱周期可测性。给出了这些可测性的充要条件,这些充要条件可通过构建观测器进行有效的判定。     

月基望远镜探测能力的地面标定

采用模拟试验在地面测试了月基望远镜(LOT)的星等探测信噪比及弥散斑能量集中度,用以验证望远镜的探测能力.与传统的通过分析CCD各项参数对噪声的影响来获得信噪比的方法不同,本文提出的方法客观、直接地通过图像信息来计算星点目标信噪比,其目标信噪比测试不确定度可优于8％.在测试弥散斑能量集中度时,通过质心算法求其弥散斑能量中心,进而提出了一种星点弥散斑高斯拟合方法来拟合弥散斑能量分布曲线.这种高斯拟合方法可使弥散斑能量集中度的测试精度提高10％.最后,通过试验测试了LOT相机星等探测信噪比及弥散斑能量集中度,验证了LOT相机+15 Mv的探测能力.     

ON THE STABILITY AND STABILIZATION OF TIME‐VARYING NONLINEAR CONTROL SYSTEMS

Many stability and stabilization problems of nonlinear time‐varying systems lead to asymptotic behavior of (–K + L)‐type systems, which consist of a K‐function and an L‐function. The stability of these systems is of fundamental importance for a series of stabilization problems of time‐varying nonlinear control systems. Even though the asymptotical stability of such systems has been used widely and (in most cases) implicitly, we do not find a rigorous proof, in the literature, and the existing proof for a particular case is questionable. Under quite general conditions, we prove that the solution of these systems tends to 0 as t →. Some generalizations are also obtained. As an immediate consequence, a general theorem is obtained for the stabilization of time‐varying systems. Using the new framework, we examine several stability and stabilization problems. First of all, for cascade systems, two sets of sufficient conditions are obtained for uniformly asymptotical stability and globally asymptotical stability, respectively. Then we consider the stability of ISS and IISS systems. A new concept, namely, strong IISS, is proposed. Several stability properties for autonomous systems are extended to time‐varying systems. Finally, we consider stabilization via detection. A rigorous proof is given for a smooth state feedback time‐varying system with weak detectability to be stabilizable by means of an observer.     

On the cardinal number of complete sets of Boolean operations†

It is shown in the literature (using the Post—Yablonsky theorem) that a complete set of Boolean operations cannot have a cardinal number greater than four. It is the object of this paper to improve this bound and prove that a complete set can have a cardinal number of at most three or, in other words, there does not exist a complete (non–redundant) set of more than three Boolean operations. The proof given here is constructive, using the Post—Yablonsky theorem, truth tables and combinatorial set theory.     

A complexity reduction approach to detectability of switching systems

In this article, we address detectability for the class of linear switching systems. We focus on some hybrid state-space decompositions of the original switching system based on hybrid invariant subspaces, which yield a complexity reduction in checking detectability. We show that the reduced system extracted from the original system is the minimal bisimilar switching system associated with it. An example is also included which shows the applicability and benefits of the proposed approach.