Discrete‐time output feedback for Markov jump systems with uncertain transition probabilities

This article addresses the output feedback control for discrete‐time Markov jump linear systems. With fully known transition probability, sufficient conditions for an internal model based controller design are obtained. For the case where the transition probabilities are uncertain and belong to a convex polytope with known vertices, we provide a sufficient LMI condition that guarantees the norm of the closed‐loop system is below a prescribed level. That condition can be improved through an iterative procedure. Additionally, we are able to deal with the case of cluster availability of the Markov mode, provided that some system matrices do not vary within a given cluster, an assumption that is suitable to deal with packet dropout models for networked control systems. A numerical example shows the applicability of the design and compares it with previous results. Copyright © 2012 John Wiley & Sons, Ltd.     

Dual approaches to strictly positive real controller synthesis with a performance using linear matrix inequalities

The synthesis of controllers that minimize a performance index subject to a strictly positive real (SPR) constraint is considered. Two controller synthesis methods are presented that are then combined into an iterative algorithm. Each method synthesizes optimal SPR controllers by posing a convex optimization problem where constraints are enforced via linear matrix inequalities. Additionally, each method fixes the controller state‐feedback gain matrix and finds an observer gain matrix such that an upper bound on the closed‐loop ‐norm is minimized and the controller is SPR. The first method retools the standard ‐optimal control problem by using a common Lyapunov matrix variable to satisfy both the criteria and the SPR constraint. The second method overcomes bilinear matrix inequality issues associated with the performance and the SPR constraint by employing a completing the square method and an overbounding technique. Both synthesis methods are used within an iterative scheme to find optimal SPR controllers in a sequential manner. Comparison of our synthesis methods to existing methods in the literature is presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Stability of a class of switched positive linear time‐delay systems

This paper addresses the problem of stability for a class of switched positive linear time‐delay systems. As first attempt, the Lyapunov–Krasovskii functional is extended to the multiple co‐positive type Lyapunov–Krasovskii functional for the stability analysis of the switched positive linear systems with constant time delay. A sufficient stability criterion is proposed for the underlying system under average dwell time switching. Subsequently, the stability result for system under arbitrary switching is presented by reducing multiple co‐positive type Lyapunov–Krasovskii functional to the common co‐positive type Lyapunov–Krasovskii functional. A numerical example is given to show the potential of the proposed techniques. Copyright © 2012 John Wiley & Sons, Ltd.     

Stochastic stability and robust stabilization of semi‐Markov jump linear systems

The semi‐Markov jump linear system (S‐MJLS) is more general than the Markov jump linear system (MJLS) in modeling some practical systems. Unlike the constant transition rates in the MJLS, the transition rates of the S‐MJLS are time varying. This paper focuses on the robust stochastic stability condition and the robust control design problem for the S‐MJLS with norm‐bounded uncertainties. The infinitesimal generator for the constructed Lyapunov function is first derived. Numerically solvable sufficient conditions for the stochastic stability of S‐MJLSs are then established in terms of linear matrix inequalities. To reduce the conservativeness of the stability conditions, we propose to incorporate the upper and lower bounds of the transition rate and meanwhile apply a new partition scheme. The robust state feedback controller is accordingly developed. Simulation studies and comparisons demonstrate the effectiveness and advantages of the proposed methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L1‐gain and L∞‐gain characterization

Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply rates are employed here for robustness and performance analysis using L₁‐gain and L_∞‐gain. Robust stability analysis is performed using integral linear constraints for which several classes of uncertainties are discussed. The approach is then extended to robust stabilization and performance optimization. The obtained results are expressed in terms of robust linear programming problems that are equivalently turned into finite dimensional ones using Handelman's theorem. Several examples are provided for illustration. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal linear estimation for continuous stochastic systems with random observation delays

This paper is concerned with the linear minimum mean square error estimation for Itô‐type differential equation systems with random delays, where the delay process is modeled as a finite‐state Markov chain. By first introducing a set of equivalent delay‐free observations and then defining two reorganized Markov chains, the estimation problem of random delayed systems is reduced to the one of delay‐free Markov jump linear systems. The estimator is derived by using the innovation analysis method based on the Itô differential formula. And the analytical solution to this estimator is given in terms of two Riccati differential equations that are of finite dimensions. Conditions for existence, uniqueness, and stability of the steady‐state optimal estimator are studied for time‐invariant cases. In this case, the obtained estimator is very easy to implement, and all calculation can be performed off line, leading to a linear time‐invariant estimator. Copyright © 2011 John Wiley & Sons, Ltd.     

Delay dependent robust stability of singular systems with additive time-varying delays

This paper considers the problem of delay-dependent robust stability for uncertain singular systems with additive time-varying delays. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are expressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.     

Modeling and robust discrete LQ repetitive control of electrically driven robots

Discrete linear quadratic control has been efciently applied to linear systems as an optimal control.However,a robotic system is highly nonlinear,heavily coupled and uncertain.To overcome the problem,the robotic system can be modeled as a linear discrete-time time-varying system in performing repetitive tasks.This modeling motivates us to develop an optimal repetitive control.The contribution of this paper is twofold.For the frst time,it presents discrete linear quadratic repetitive control for electrically driven robots using the mentioned model.The proposed control approach is based on the voltage control strategy.Second,uncertainty is efectively compensated by employing a robust time-delay controller.The uncertainty can include parametric uncertainty,unmodeled dynamics and external disturbances.To highlight its ability in overcoming the uncertainty,the dynamic equation of an articulated robot is introduced and used for the simulation,modeling and control purposes.Stability analysis verifes the proposed control approach and simulation results show its efectiveness.     

一种相控阵天线安装精度检测与校准

文中论述了一种相控阵雷达天线安装后的精度检测方法。按照雷达天线安装后的几何形态,采用光学测量仪器进行相关的数据采集,建立检测的数学模型,利用线性回归法以及最小二乘法进行数据拟合,计算出安装后雷达天线底面与水平面的最大夹角和天线边缘与正北方向的夹角,并进行了试验误差评估和分析,依据检测数据对雷达天线的水平和方位角度进行校...     

钱江通道段河床最大冲刷深度的综合分析

钱江通道位于钱塘江河口的强涌潮区域,在洪潮水动力作用下河床冲淤剧烈.极端水动力作用下河床的冲刷深度是过江隧道工程建设的关键技术问题之一.本文基于河床演变分析、动床数值模拟、动床物理模型试验、沉积物分析等手段进行研究.首先建立了钱江通道过江隧道河段洪、潮水流冲刷深度的预测模型,经钱塘江河口的实测地形、水流泥沙及河床冲淤等资料的验证.在此基础上预测了过江隧道断面在极端水动力作用下最大冲刷深度,并与沉积物分析方法进行比较,四种研究方法所得的结果定性定量基本合理,进一步表明了预测模型的可靠性,预测的最大冲刷深度可为过江隧道的合理埋设提供参考依据.