Robust Stochastic Stability and Control for Uncertain Singular Markovian Jump Systems with Multiplicative Noise

This paper focuses on the problems of robust stability and stabilization and robust control for uncertain singular Markovian jump systems with (x,v)‐dependent noise. The parameter uncertainties appearing in state, input, disturbance as well as diffusion terms are assumed to be time‐varying but norm‐bounded. Based on the approach of generalized quadratic stability, the memoryless state feedback controller is designed for the robust stabilization problem, which ensures that the resulting closed‐loop system has an impulse‐free solution and is asymptotically stable in the mean square. Furthermore, the results of robust control problem are derived. The desired state feedback controller is presented, which not only meets the requirement of robust stabilization but also satisfies a prescribed performance level. The obtained results are formulated in terms of strict LMIs. What we have obtained can be viewed as corresponding extensions of existing results on uncertain singular systems. A numerical example is finally given to demonstrate the application of the proposed method.     

Global adaptive stabilization for high‐order uncertain time‐varying nonlinear systems with time‐delays

This paper focuses on the adaptive stabilization problem for a class of high‐order nonlinear systems with time‐varying uncertainties and unknown time‐delays. Time‐varying uncertain parameters are compensated by combining a function gain with traditional adaptive technique, and unknown multiple time‐delays are manipulated by the delicate choice of an appropriate Lyapunov function. With the help of homogeneous domination idea and recursive design, a continuous adaptive state‐feedback controller is designed to guarantee that resulting closed‐loop systems are globally uniformly stable and original system states converge to zero. The effectiveness of the proposed control scheme is illustrated by the stabilization of delayed neural network systems. Copyright © 2016 John Wiley & Sons, Ltd.     

A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation

This paper is concerned with semi-global stabilization of discrete-time linear periodic systems subject to actuator saturation. Provided that the open loop characteristic multipliers are within the closed unit circle, a low gain feedback design approach is proposed to solve the problem by state feedback. Our approach is based on the solution to a parametric discrete-time periodic Lyapunov equation. The proposed approaches not only generalize the corresponding results for time-invariant systems to periodic systems, but also reveal some important intrinsic properties of this class of periodic matrix equations. A numerical example is worked out to illustrate the effectiveness of the proposed approaches.     

Reachability and stabilization of discrete-time affine systems with disturbances

This paper studies the fundamental problems: whether an affine system affected by additive disturbances is robustly transferable from a source set (simplex) to a target set (polytope) and whether it is robustly stabilizable with its state constrained in a simplex. First, a necessary and sufficient condition is derived for the existence of affine feedback control that solves the robust reachability problem. Further investigation is provided for two situations relying on whether the union of the source set and the target set is convex or non-convex. For the former one, a necessary and sufficient condition is obtained in the form of linear inequalities, while for the latter, several computationally feasible sufficient conditions are found. Second, we show that robust stabilization subject to a state constraint is equivalent to find a feasible solution to a linear equation. Once it is known that either of the problems has a solution by checking the derived conditions, design of control laws is then straightforward.     

Vision-based control for rigid body stabilization

This paper addresses the problem of stabilizing to a desired equilibrium point an eye-in-hand system, which consists of a single camera mounted on a rigid body free to move on . It is assumed that there is a collection of landmarks fixed in the environment and that the image coordinates of those landmarks are provided to the system by an on-board CCD camera. The proposed method addresses not only the problem of stabilization but also that of maintaining feature visibility along the system’s trajectory. The resulting solution consists of a feedback control law based on the current and desired image coordinates and reconstructed attitude and depth ratio information, which guarantees that (i) the desired equilibrium point is an almost global attractor; (ii) a set of necessary conditions for feature visibility holds throughout the system’s trajectories; and (iii) the image of a predefined feature point is kept inside the camera’s field of view.     

一类相似组合大系统的线性反馈镇定

研究相似组合大系统的二次镇定问题,利用系统的特殊结构导出其二次可稳的条件及（分散）状态反馈控制律律的求解方法,其特点是只需求解两个低阶Ｒｉｃｃａｔｉ方程或不等式,大大简化了控制器的设计。     

差动吸收式SO2光纤传感器的研究

本文基于气体的窄带光吸收特性 ,研究了 SO2 气体浓度与载波光强的关系 ,在此基础上 ,设计了一种检测该气体浓度的差动光纤传感器及其系统 ,对改善仪器精度等特性指标的主要因素进行分析。实验结果表明该仪器具有较高的灵敏度和精度。     

A note on the problem of semiglobal practical stabilization of uncertain nonlinear systems via dynamic output feedback

It is known that if a system can be (robustly) globally asymptotically stabilized by means of a feedback that is driven by functions that are uniformly completely observable (UCO), then this system can be practically semiglobally stabilized by means of (possibly dynamic) output feedback. This papers discusses a significant structural hypothesis under which the existence of a dynamic feedback driven by UCO functions is guaranteed. The class of systems which satisfy this hypothesis includes any stabilizable and detectable linear system and any relative degree one nonlinear system which is stabilizable by dynamic output feedback. In particular, the hypothesis does not require the system to be minimum phase.     

Stabilization of Dynamic Systems Providing Additional Properties of Transients

The problem is to construct bounded stabilization feedbacks that provide additional properties of transient processes (degree of stability, oscillation, absence of overshoot, monotonicity). The problem is solved by means of optimal control methods. The results are illustrated by an example of stabilization of a dynamic fourth-order system.     

一类结构不确定的非线性相似组合系统的分散鲁棒镇定

首先描述了两个控制系统的相似性概念,然后讨论了一类结构不确定的非线性相似组合系统的鲁棒镇定问题,设计出一类分散控制器,这种控制器由线性和非线性两部分组成。结果表明,相似结构确定可以简化组合系统鲁棒镇定的判据,最后的算例和仿真表明了本文结论的有效性。