非结构化不确定性矩阵的极点鲁棒集聚于优良飞行性能区域的分析

分析了不确定性矩阵的极点鲁棒集聚于飞机的一个优良飞行性能区域.该区域是一个特殊的非Ω可变换区域,它是一个圆环和一个水平带域的位于左半平面的交集,由试验知道位于这个区域的控制系统极点提供了飞机优良的飞行性能.由于广义Lyapunov理论不适用于非Ω可变换区域,因此本文应用Rayleigh原理和范数理论进行分析,所考虑的不确定性是非结构化的.所得结果可应用于飞机、飞行器和空间站等鲁棒分析.     

Comments on “Perturbation bounds for root-clustering oflinear systems in a specified second order subregion”

This paper comments on the results of the above mentioned paper by Bakker-Luo-Johnson (ibid. vol.40 (1995)). We note that Theorems 3.1 and 4.1 are incorrectly stated, i.e., they are not valid for the non-Ω-transformable regions. The results cannot cover the ride quality region listed in Table 1 since it is a non-Ω-transformable region     

Observer-based controller for robust pole clustering in a vertical strip and disturbance rejection in structured uncertain systems

This paper presents an observer-based multi-objective robust feedback controller to achieve robust pole clustering within a vertical strip and disturbance rejection with an H_∞-norm constraint for the uncertain linear systems. The systems of interest include both matched and mismatched uncertain linear systems with structured uncertainties existing in both the system and input matrices. The controller is obtained by solving two Riccati equations (one for the controller and the other for the observer) and checking three conditions (two for robust pole clustering). A set of tuning parameters is incorporated to enhance flexibility in finding the controller. © 1998 John Wiley & Sons, Ltd.     

离散广义系统的鲁棒稳定性

针对具有结构不确定性的离散广义系统,提出了一种新的鲁棒稳定性分析方法;得 到了使所考虑系统鲁棒稳定的条件,该条件保证对所有容许的结构摄动,离散广义系统正则、 因果且稳定;并进一步得到了所考虑系统具有鲁棒极点集的条件.     

Model reference tracking control of an aircraft: a robust adaptive approach

This work presents the design and the corresponding analysis of a nonlinear robust adaptive controller for model reference tracking of an aircraft that has parametric uncertainties in its system matrices and additive state- and/or time-dependent nonlinear disturbance-like terms in its dynamics. Specifically, robust integral of the sign of the error feedback term and an adaptive term is fused with a proportional integral controller. Lyapunov-based stability analysis techniques are utilised to prove global asymptotic convergence of the output tracking error. Extensive numerical simulations are presented to illustrate the performance of the proposed robust adaptive controller.     

Analysis and applications of robust nonsingularity problem usingthe structured singular value

This note uses the structured singular value technique to solve the robust nonsingularity analysis problem for matrices with unstructured and/or quadratically coupled structured uncertainties. With the ready μ-analysis tools, a new approach is proposed for finding a set of uncertainties within which the perturbed matrix keeps nonsingularity. Applications and examples in robust control theory are given to show the usefulness and the practicality of the proposed approach     

On the robustness of uncertain time-delay systems with structured uncertainties

This paper considers the robust stability and robust performance of uncertain delay systems subject to possibly structured uncertainties using structured singular values with phase information. Computationally efficient sufficient conditions for robust stability and performance problem are derived.     

Robust H∞ control for uncertain discrete-time systems with circular pole constraints

This paper investigates the problem of robust H_∞ control for uncertain discrete-time systems with circular pole constraints. The system under consideration is subject to norm-bounded time-invariant uncertainties in both the state and input matrices. The problem we address is to design state feedback controllers such that the closed poles are located within a prespecified circular region, and the H_∞ norm of the closed-loop transfer function is strictly less than a given positive scalar for all admissible uncertainties. By introducing the notion of quadratic d stabilizability with an H_∞ norm-bound, the problem is solved. Necessary and sufficient conditions for quadratic d stabilizability with an H_∞ norm-bound are derived. Our results can be regarded as extensions of existing results on robust H_∞ control and robust pole assignment of uncertain systems.     

不确定广义系统的圆形区域极点配置

考虑不确定连续或离散广义系统的圆形区域极点配置问题, 目的是设计状态反 馈控制律, 使得闭环系统正则, 无脉冲(连续广义系统情形)或因果(离散广义系统情形), 且 闭环极点位于一给定的圆形区域内. 给出了所期望的状态反馈控制律存在的充分条件及其解 析表达式.     

A new design of robust filters for uncertain systems

In this paper, a structured polynomial parameter-dependent approach is proposed for robust H₂ filtering of linear uncertain systems. Given a stable system with parameter uncertainties residing in a polytope with s vertices, the focus is on designing a robust filter such that the filtering error system is robustly asymptotically stable and has a guaranteed estimation error variance for the entire uncertainty domain. A new polynomial parameter-dependent idea is introduced to solve the robust H₂ filtering problem, which is different from the quadratic framework that entails fixed matrices for the entire uncertainty domain, or the linearly parameter-dependent framework that uses linear convex combinations of s matrices. This idea is realized by carefully selecting the structure of the matrices involved in the products with system matrices. Linear matrix inequality (LMI) conditions are obtained for the existence of admissible filters and based on these, the filter design is cast into a convex optimization problem, which can be readily solved via standard numerical software. Both continuous and discrete-time cases are considered. The merit of the methods presented in this paper lies in their less conservatism than the existing robust filter design methods, as shown both theoretically and through extensive numerical examples.     

On robust stabilization of Markovian jump systems with uncertain switching probabilities

This brief paper is concerned with the robust stabilization problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertain Markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix. First, a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities. Then, a sufficient condition is proposed for the design of robust state-feedback controllers. A globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively. Finally, a numerical simulation is used to illustrate the developed theory.     

Robust stability of a special class of polynomial matrices with control applications

The robust stability problem of uncertain continuous-time systems described by higher-order dynamic equations is considered in this paper. Previous results on robust stability of Metzlerian matrices are extended to matrix polynomials, with the coefficient matrices having exactly the same Metzlerian structure. After defining the structured uncertainty for this class of polynomial matrices, we provide an explicit expression for the real stability radius and derive simplified formulae for several special cases. We also report on alternative approaches for investigating robust Hurwitz stability and strong stability of polynomial matrices. Several illustrative examples throughout the paper support the theoretical development. Moreover, an application example is included to demonstrate uncertainty modeling and robust stability analysis used in control design.     

Robust stability and performance via fixed-order dynamic compensation with guaranteed cost bounds

A feedback control-design problem involving structured plant parameter uncertainties is considered. Two robust control-design issues are addressed. The Robust Stability Problem involves deterministic bounded structured parameter variations, while the Robust Performance Problem includes, in addition, a quadratic performance criterion averaged over stochastic disturbances and maximized over the admissible parameter variations. The optimal projection approach to fixed-order, dynamic compensation is merged with the guaranteed cost control approach to robust stability and performance to obtain a theory of full- and reduced-order robust control design. The principle result is a sufficient condition for characterizing dynamic controllers of fixed dimension which are guaranteed to provide both robust stability and performance. The sufficient conditions involve a system of modified Riccati and Lyapunov equations coupled by an oblique projection and the uncertainty bounds. The full-order result involves a system of two modified Riccati equations and two modified Lyapunov equations coupled by the uncertainty bounds. The coupling illustrates the breakdown of the separation principle for LQG control with structured plant parameter variations. Supported in part by the Air Force Office of Scientific Research under Contract F49620-86-C-0002.     

Robust H-infinity control for constrained uncertain systems and its application to active suspension

This paper presents an LMI based robust H-infinity control scheme for constrained systems with normbounded uncertainties.The uncertainties are incorporated in the evaluation of the H-infinity norm and the time-domain constraints.The robust closed-loop properties inclusive of stability,H-infinity performance and the satisfaction of the timedomain constraints are discussed.Analysis and simulation results for a 2 DOF quarter-car model show possible improvements on ride comfort,while robustly respecting safety related constraints such as good road holding,limited suspension strokes and actuator saturation.     

Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays

This paper concerns the problem of the delay-dependent robust stability of neutral systems with mixed delays and time-varying structured uncertainties. A new method based on linear matrix inequalities is presented that makes it easy to calculate both the upper stability bounds on the delays and the free weighting matrices. Since the criteria take the sizes of the neutral- and discrete-delays into account, it is less conservative than previous methods. Numerical examples illustrate both the improvement this approach provides over previous methods and the reciprocal influences between the neutral- and discrete-delays.     

A less conservative robust stability criteria for uncertain neutral systems with mixed delays

This paper is concerned with the problem of the delay-dependent robust stability of neutral systems with mixed delays and time-varying structured uncertainties. By considering the cross-terms with additional design parameters, a complete form of Lyapunov–Krasovskii functional is constructed. Then some free weighting matrices are introduced, and a sufficient stability condition is obtained in terms of linear matrix inequalities. The obtained criterion is dependent on the sizes of neutral delay and discrete delay and are less conservative than those produced by previous approaches. Numerical examples are given to illustrate both the improvement the proposed method provides over some existing ones and the relationship between the neutral- and discrete-delay.     

Delay-dependent criteria for robust stability of time-varying delay systems

This paper deals with the problem of delay-dependent robust stability for systems with time-varying structured uncertainties and time-varying delays. Some new delay-dependent stability criteria are devised by taking the relationship between the terms in the Leibniz-Newton formula into account. Since free weighting matrices are used to express this relationship and since appropriate ones are selected by means of linear matrix inequalities, the new criteria are less conservative than existing ones. Numerical examples suggest that the proposed criteria are effective and are an improvement over previous ones.     

Robust pole assignment for systems with parameters

In this paper we investigate issues related to the control of linear multivariate systems which contain structured, parametric-type uncertainties. The objective is to construct parameter-independent proper compensators that provide ‘robust control’. Specifically, we consider the question of robust pole assignment. Systems are described by matrix fraction representations which involve a structured parametric form of uncertainty. We suggest conditions for robust pole assignability and demonstrate how to construct the required proper compensators. For the problem considered, we show that the class of systems which satisfy these conditions is quite large and we include results on generic solvability. The method is demonstrated by a physical example.