Robust Stability of Multivariate Polynomials, Part 2: Polytopic Coefficient Variations

This paper deals with robustness of stability propety of a class of multivariate polynomials, recently introduced in kharjt. The aim is to show the use of this class when analyzing stability of mutivariate polynomial families with polytopic coefficient variations. This study is developed on the basis of some known stability results for polytopic families of scattering Hurwitz stable (SHS) as well as strict sense stable (SSS) multivariate polynomials.     

Controllable and Autonomous nD Linear Systems

The theory of multidimensional systems suffers in certain areas from a lack of development of fundamental concepts. Using the behavioural approach, the study of linear shift-invariant nD systems can be encompassed within the well-established framework of commutative algebra, as previously shown by Oberst. We consider here the discrete case. In this paper, we take two basic properties of discrete nD systems, controllability and autonomy, and show that they have simple algebraic characterizations. We make several non-trivial generalizations of previous results for the 2D case. In particular we analyse the controllable--autonomous decomposition and the controllable subsystem of autoregressive systems. We also show that a controllable nD subsystem of is precisely one which is minimal in its transfer class.     

Robust hurwitz property of bivariate polynomials in the space of Markov parameters

Markov parameters and the associated stability criterion were first introduced for continuous-time real polynomials. Recently, robust stability of such polynomials was considered in Markov parameters space, where efficient robust stability tests were obtained based on the Markov theorem. This motivated the authors to extend the above idea, and develop Markov parameters and the associated stability criterion for more general types of polynomials such as complex continuous-time as well as real and complex discrete-time polynomials. In this paper a procedure is given for evaluating the maximum allowable perturbations in the Markov parameters of a complex coefficient univariate as well as real coefficient bivariate polynomials so that the strict Hurwitz property remains invariant.     

多胞型二维多项式的Schur稳定性

本文提出多胞型二维多项式的Schur稳定的充分必要条件。我们揭示多胞型二维多项式的系数具有线性仿射特性。基于这一仿射特性,将多胞型二维多项式视为具有复变系数的多胞型一维多项式,我们证明多胞型二维多项式的稳定性可由其有限的棱边多项式的稳定性保证。我们提供了一种棱边多项式的稳定性检验算法。     

Computation of stability radius for families of bivariate polynomials

In this paper we apply optimization techniques to the problem of robust stability of a family of bivariate polynomials under affine coefficient perturbations. The size of the perturbations is measured by a convex function. In this paper we concentrate onl ^p weighted norms, for three special casesp = 1,p = 2, andp = . Necessary and sufficient conditions for robust stability are provided. Evaluation of the stability radius is reduced to a minimization problem in two-dimensional space. The results open the door to the development and implementation of reliable and efficient algorithms for the computation of the stability radius.     

无线网络拥塞控制中流体流模型的Hopf分岔及其稳定性

该文对一个用于无线网络拥塞控制算法设计的具有通信时延的流体流模型进行Hopf分岔分析,以通信时延作为分岔参数,证明此模型Hopf分岔的存在性,并应用中心流形和规范型理论推导出确定 Hopf 分岔方向和分岔周期解稳定性的计算公式,数值仿真验证了结论的有效性。     

基于鲁棒稳定的闭环激磁电源幅值回路设计

保证系统鲁棒稳定,同时满足系统性能指标要求始终是控制设计的目标。该文根据转台测角系统对激磁电源稳定性和性能指标的要求,提出了采用H优化控制理论,以鲁棒稳定为基础的闭环激磁电源幅值回路设计的方法,讨论了H控制器的求解过程。经四个转台长期使用验证该设计方法的有效性和合理性,完全满足了高精度转台的需要。     

Gain-scheduled robust control for lateral stability of four-wheel-independent-drive electric vehicles via linear parameter-varying technique

This paper proposes a robust gain-scheduled H_∞ controller for lateral stability control of four-wheel-independent-drive electric vehicles via linear parameter-varying technique. The controller aims at tracking the desired yaw rate and vehicle sideslip angle by controlling the external yaw moment. In the design of controller, uncertain factors such as vehicle mass and tire cornering stiffness in vehicle lateral dynamics are represented via the norm-bounded uncertainty. To address the importance of time-varying longitudinal velocity for vehicle lateral stability control, a linear parameter-varying polytopic vehicle model is built, and the built vehicle model depends affinely on the time-varying longitudinal speed that is described by a polytope with finite vertices. In order to reduce conservative, the hyper-rectangular polytope is replaced by a hyper-trapezoidal polytope. Simultaneously, the quadratic D-stability is also applied to improve the transient response of the closed-loop system. The resulting gain-scheduling state-feedback controller is finally designed, and solved utilizing a set of linear matrix inequalities derived from quadratic H_∞ performance and D-stability. Simulations using Matlab/Simulink-Carsim® are carried out to verify the effectiveness of the proposed controller with a high-fidelity, CarSim®, full-vehicle model. It is found from the results that the robust gain-scheduled H_∞ controller suggested in this paper provides improved vehicle lateral stability, safety and handling performance.     

稳相电缆弯曲相位稳定性测试方法的比较

稳相电缆的弯曲相位稳定性指标对于相敏系统中的信号传输而言至关重要。为了精确测得电缆弯曲前后相位的变化量,本文介绍三种电缆弯曲相位稳定性的测试方法,并通过实例的测试对其进行比较和分析。     

An improved LMI-based criterion for the design of optimal guaranteed cost controller for 2-D discrete uncertain systems

An improved criterion for the design of optimal static-state feedback guaranteed cost controller for two-dimensional (2-D) discrete uncertain systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model is proposed. The design problem of the optimal guaranteed cost controller is formulated as a convex optimization problem with linear matrix inequality (LMI) constraints. The proposed method yields tighter upper bound of the closed-loop cost function as compared to a recently reported method.     

复合材料在热真空下的尺寸稳定性测试方法

航天光学遥感器在轨运行时的环境与地面装调时有很大差异,对于采用复合材料的遥感器而言,在轨运行时由于材料受湿气解析的影响其几何尺寸将发生变化,进而影响遥感器的成像质量.因此,模拟在轨环境下复合材料几何尺寸稳定性测试,分析其在轨条件下的几何尺寸变形是十分必要的.提出了一种在热真空环境下,采用激光双频干涉原理对复合材料几何尺寸变形量的高精度测试方法,对该方法进行了方案验证与精度分析.针对采用碳纤维蒙皮/铝蜂窝夹层结构复合材料的某相机前镜筒进行了实际的热真空环境下几何尺寸变形量测试.结果表明,试验数据与理论数值在数量级上相同,提出的测试方案可行,为复合材料模拟在轨环境下几何尺寸变形量提供了一种测试手段.     

LMI approach to stability of 2D positive systems

The asymptotic stability of positive 2D linear systems with delays (systems of order higher one) described by the Roesser model, the 2D Fornasini–Marchesini models and the general model is addressed. It is shown that the linear matrix inequalities (LMIs) can be used to checking the asymptotic stability of the positive 2D systems. Using LMI approach necessary and sufficient conditions for the asymptotic stability of the positive 2D systems with delays are established. The efficiency of the LMI approach is demonstrated on numerical examples of positive 2D linear systems with delays.

An algorithm for stability determination of two-dimensional delta-operator formulated discrete-time systems

The recent interest in delta-operator (or, -operator) formulated discrete-time systems (or, -systems) is due mainly to (a) their superior finite wordlength characteristics as compared to their more conventional shift-operator (or,q-operator) counterparts (or,q-systems), and (b) the possibility of a more unified treatment of both continuous- and discrete-time systems. With such advantages, design, analysis, and implementation of two-dimensional (2-D) discrete-time systems using the -operator is indeed warranted. Towards this end, the work in this paper addresses the development of an easily implementabledirect algorithm for stability checking of 2-D -system transfer function models.Indirect methods that utilize transformation techniques are not pursued since they can be numerically unreliable. In developing such an algorithm, a tabular form for stability checking of -system characteristic polynomials with complex-valued coefficients and certain quantities that may be regarded as their corresponding Schur-Cohn minors are also proposed.     

Matrix conditions for the stability of 2D dynamics

The stability of two-dimensional (2D) dynamics is studied from the viewpoint of quadratic Lyapunov stability. An already-known simple sufficient condition for the stability of 2D dynamics is first reconsidered by introducing a new notion about the stability of a pair of matrices. It is interpreted as a condition for step-by-step contractive stability in a suitably selected state coordinate. In this direction, some necessary and sufficient conditions for the stability of 2D dynamics are shown in detail. The meaning of the original simple sufficient condition is further clarified in this extension. A condition for being free of overflow oscillations in saturation arithmetic is added as a special topic of the Lyapunov stability of 2D dynamics.     

On the stability preserving property of the double bilinear transformation on a class of 2-D transfer functions

This paper addresses the BIBO (bounded-input bounded-output) stability of a class of discrete 2-D quarter-plane filters in the presence of nonessential singularities of the second kind (NSSK's) on the unit bidisk. Conditions under which the double bilinear transformation (DBT) preserves stability are derived. The results presented here also extend the class of systems whose stability can be predicted. Use of the inverse DBT to produce a continuous equivalent of the discrete 2-D transfer function allows easy application of a continuous-domain equivalent of a criterion developed by Dautov. The necessary and sufficient condition for stability derived in this work provides a simple check for the class of systems under consideration. From this class of systems, it is also possible to construct stable pairs of mutually inverse transfer functions.     

LD组件温度稳定性设计

为了研究热电致冷器模块对半导体激光器温度控制系统稳定性的影响,采用模拟比例-积分-微分(PID)网络作为系统的控制器,通过对PID控制网络的调整,优化了热电致冷模块的响应,并根据调整后的PID控制网络及各组成部分的特性建立系统的数学模型,分析了系统对单位阶跃输入的稳态误差和稳定性。经仿真比较,结果表明,优化后的系统具有很好的瞬态特性和稳定性。     

Robust stability of multidimensional difference equations with shift-variant coefficients

This paper addresses the asymptotic stability of multidimensional systems represented by first hyperquadrant causal linear difference equations whose coefficients are shift-varying. The results extend previous 1-D results, and include the derivation of a fixed region of stability in the parameter space, as well as a sequence of shift-variant parameter regions. In the case of a fixed parameter region, the largest stable hyperdiamond centered at the origin will be obtained. For the shift-variant case, it will be shown that the instantaneous stable parameter region always includes this hyperdiamond.     

高功率热稳定及不对准低敏感TEM00模谐振腔设计

针对全固态激光器高功率运转时存在的热效应问题,本文从热稳定腔理论出发,给出了凸凹热稳定及失谐不敏感腔的设计方法和步骤,并以Nd：YAG激光器为例,用曲线图解法求出最佳腔参数。这种凸凹腔型具有基模体积大,热稳定性好,不对准灵敏度低的优点。     

Design and implementation of a robust and nonlinear flight control system for an unmanned helicopter

In this work, we focus on the design and implementation of a robust flight control system for an unmanned helicopter. A comprehensive nonlinear model for an unmanned helicopter system, which is built by our research team at the National University of Singapore, is first presented. A three-layer control architecture is then adopted to construct an automatic flight control system for the aircraft, which includes (1) an inner-loop controller designed using the H_∞ control technique to internally stabilize the aircraft and at the same time yield good robustness properties with respect to external disturbances, (2) a nonlinear outer-loop controller to effectively control the helicopter position and yaw angle in the overall flight envelope, and lastly, (3) a flight-scheduling layer for coordinating flight missions. Design specifications for military rotorcraft set for the US army aviation are utilized throughout the whole process to guarantee a top level performance. The result of actual flight tests shows our design is very successful. The unmanned helicopter system is capable of achieving the desired performance in accordance with the military standard under examination.