Robust H∞ Filter Design for 2D Discrete Systems in Roesser Model

This paper investigates the robust H∞ filtering problem for uncertain two-dimensional (2D) systems described by the Roesser model. The parameter uncertainties considered in this paper are assumed to be of polytopie type. A new structured polynomi-ally parameter-dependent method is utilized, which is based on homogeneous polynomially parameter-dependent matrices of arbitrary degree. The proposed method includes results in the quadratic framework and the linearly parameter-dependent framework as special cases for zeroth degree and first degree, respectively. A numerical example illustrates the feasibility and advantage of the proposed filter design methods.     

H∞ Control of Discrete-Time Systems With Multiple Input Delays

This paper is concerned with the finite horizon H_infin full-information control for discrete-time systems with multiple control and exogenous input delays. We first establish a duality between the H_infin full-information control and the H₂ smoothing of a stochastic backward system in Krein space. Like the duality between the linear quadratic regulation (LQR) of linear systems without delays and the Kalman filtering, the established duality allows us to address complicated multiple input delay problems in a simple way. Indeed, by applying innovation analysis and standard projection in Krein space, in this paper we derive conditions under which the H_infin full-information control is solvable. An explicit controller is constructed in terms of two standard Riccati difference equations of the same order as the original plant (ignoring the delays). As special cases, solutions to the H_infin state feedback control problem for systems with delays only in control inputs and the H_infin control with preview are obtained. An example is given to demonstrate the effectiveness of the proposed H_infin control design     

Fixed-Order Robust H∞ Controller Design With Regional Pole Assignment

In this technical note, the problem of designing fixed-order robust H_infin controllers is considered for linear systems affected by polytopic uncertainty. A polynomial method is employed to design a fixed-order controller that guarantees that all the closed-loop poles reside within a given region of the complex plane. In order to utilize the freedom of the controller design, an H_infin performance specification is also enforced by using the equivalence between robust stability and H_infin norm constraint. The design problem is formulated as a linear matrix inequality (LMI) constraint whose decision variables are controller parameters. An illustrative example demonstrates the feasibility of the proposed design methods.     

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.     

Approaches to Robust Filtering Design of Discrete Time Fuzzy Dynamic Systems

This paper presents two filter design methods for discrete time fuzzy dynamic systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting filtering error system is globally stable with guaranteed H_infin or generalized H₂ performance and the filter gains can be obtained by solving a set of linear matrix inequalities. Two simulation examples are also given to illustrate the performance of the proposed approaches.     

Robust filtering for uncertain linear systems: LMI based methods with parametric Lyapunov functions

This paper addresses the design of robust filters for linear continuous-time systems subject to parameter uncertainty in the state-space model. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. Two methods based on parameter-dependent Lyapunov functions are proposed for designing linear stationary asymptotically stable filters that assure asymptotic stability and a guaranteed performance, irrespective of the uncertain parameters. The proposed filter designs are given in terms of linear matrix inequalities which depend on a scalar parameter that should be searched for in order to optimize the filter performance.     

Robust fault detection with missing measurements

This paper investigates the problem of robust fault detection for uncertain systems with missing measurements. The parameter uncertainty is assumed to be of polytopic type, and the measurement missing phenomenon, which appears typically in a network environment, is modelled by a stochastic variable satisfying the Bernoulli random binary distribution. The focus is on the design of a robust fault detection filter, or a residual generation system, which is stochastically stable and satisfies a prescribed disturbance attenuation level. This problem is solved in the parameter-dependent framework, which is much less conservative than the quadratic approach. Both full-order and reduced-order designs are considered, and formulated via linear matrix inequality (LMI) based convex optimization problems, which can be efficiently solved via standard numerical software. A continuous-stirred tank reactor (CSTR) system is utilized to illustrate the design procedures.     

Nonfragile H∞ Control for Uncertain Neutral Systems With Time-Varying Delays via the LMI Optimization Approach

The nonfragile H_infin control problem for a neutral system with time-varying delays is considered. Delay-dependent criteria are proposed to guarantee the stabilization and disturbance attenuation of systems. A linear matrix inequality optimization approach is used to solve the nonfragile H_infin control problem. Nonfragile H _infin control for an unperturbed neutral system is investigated first. Then, nonfragile H_infin control for an uncertain neutral system is derived directly from the unperturbed case. Finally, two examples are illustrated to show the improvement of this correspondence     

Parameter-dependent robust H ∞ filter design for uncertain discrete-time systems with quantized measurements

This paper deals with the problem of parameter-dependent robust H _∞ filter design for uncertain discrete-time systems with output quantization. The uncertain parameters are supposed to reside in a polytope. The system outputs are quantized by a memoryless logarithmic quantizer before being transmitted to a filter. Attention is focused on the design of a robust H _∞ filter to mitigate quantization effects and ensure a prescribed H _∞ noise attenuation level. Via introducing some slack variables and using the parameter-dependent Lyapunov function, sufficient conditions for the existence of a robust H _∞ filter are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.     

Design and analysis of discrete-time robust Kalman filters

In this paper, the problem of finite and infinite horizon robust Kalman filtering for uncertain discrete-time systems is studied. The system under consideration is subject to time-varying norm-bounded parameter uncertainty in both the state and output matrices. The problem addressed is the design of linear filters having an error variance with an optimized guaranteed upper bound for any allowed uncertainty. A novel technique is developed for robust filter design. This technique gives necessary and sufficient conditions to the design of robust quadratic filters over finite and infinite horizon in terms of a pair of parameterized Riccati equations. Feasibility and convergence properties of the robust quadratic filters are also analyzed.     

基于依参数分离算子的鲁棒可靠滤波器设计

针对凸面体不确定系统并考虑传感器发生故障的情况, 基于二次型分离算子进行了鲁棒可靠滤波器设计的研究. 利用不确定系统鲁棒镇定时的拓扑解释, 采用分离算子将不含故障描述的系统矩阵与故障描述矩阵进行解耦, 从而获得对故障不敏感的鲁棒可靠滤波器. 为进一步降低设计的保守性, 文中还给出了一种依参数分离算子的滤波器存在条件, 并将滤波器设计转化为线性矩阵不等式 (LMIs) 表述的凸优化问题. 仿真实例验证了文中所提出设计方法的有效性.     

Control Synthesis of Singularly Perturbed Fuzzy Systems

This paper considers the problem of designing stabilizing and H_infin controllers for nonlinear singularly perturbed systems described by Takagi-Sugeno fuzzy models with the consideration of the bound of singular perturbation parameter e. For the synthesis problem of simultaneously designing the bound of e and stabilizing or H_infin controllers, linear matrix inequalities (LMI)- based methods are presented. For evaluating the upper bound of e subject to stability or a prescribed H_infin performance bound constraint for the resulting closed-loop system, sufficient conditions are developed, respectively. For the stabilizing and H_infin control synthesis without the consideration of improving the bound of e, new design methods are also given in terms of solutions to a set of LMIs. Examples are given to illustrate the efficiency of the proposed methods.     

A New $H_{{bm infty}}$ Stabilization Criterion for Networked Control Systems

This note is concerned with robust H_infin control of linear networked control systems with time-varying network-induced delay and data packet dropout. A new Lyapunov-Krasovskii functional, which makes use of the information of both the lower and upper bounds of the time-varying network-induced delay, is proposed to drive a new delay-dependent H_infin stabilization criterion. The criterion is formulated in the form of a non-convex matrix inequality, of which a feasible solution can be obtained by solving a minimization problem in terms of linear matrix inequalities. In order to obtain much less conservative results, a tighter bounding for some term is estimated. Moreover, no slack variable is introduced. Finally, two numerical examples are given to show the effectiveness of the proposed design method.     

Quadratic guaranteed cost control for uncertain dissipative models: A Riccati equation approach

The problem of H₂ guaranteed cost control and dynamic output-feedback for linear uncertain systems with dissipative uncertainty is addressed. The problem of robust H₂ synthesis has been open for the last two decades. In this paper, a problem of H₂ quadratic guaranteed cost control is defined for uncertain systems affected by LTI quadratic dissipative model uncertainty. A necessary and sufficient condition of quadratic stabilizability via output-feedback is derived in terms of two coupled parameter-dependent Riccati equations. Then, a method is given to design controllers which minimize an upper bound for the worst-case H₂ norm of the uncertain system. It therefore assesses a guaranteed level of robust performance where in literature, only nominal performance is ensured in most cases. A reliable numerical iterative procedure based on Riccati solvers and one-dimensional convex parameter search is provided. With this uncertainty modelling and the developed numerical procedure, we hope to reduce the usual conservatism of quadratic designs.     

Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals

This paper considers the problem of robust stability and robust stabilization for linear systems with a constant time-delay in the state and subject to real convex polytopic uncertainty. First of all, for robust stability problem, we exploit new matrix inequalities characterization of delay-dependent quadratic stability results, demonstrate that it allows the use of parameter-dependent Lyapunov functionals, and develop control design methods based on linear matrix inequalities (LMIs) for solving the robust control problem. Next, the problem of determining the maximum time-delay under which the system remains stable is cast into a generalized eigenvalue problem and thus solved by LMI techniques. Finally, illustrative examples are given to demonstrate the advantage of these new representations.     

Synthesis of minimax optimal controllers for uncertain time-delay systems with structured uncertainty

This paper is concerned with the design of robust state feedback controllers for a class of uncertain time-delay systems. The uncertainty is assumed to satisfy a certain integral quadratic constraint. The controller proposed is a minimax optimal controller in the sense that it minimizes the maximum value of a corresponding linear quadratic cost function over all admissible uncertainties. The controller leads to an absolutely stable closed loop uncertain system and is constructed by solving a finite dimensional parameter-dependent algebraic Riccati equation.     

不确定系统混合H2/H∞鲁棒控制的直接迭代LMI方法

设计多胞型不确定系统的控制器时,引入附加变量能够减小设计保守性,但这会使线性矩阵不等式(LMI)的维数大大增加,控制器难以求解.本文阐述了一种基于直接迭代线性矩阵不等式(DILMI)方法的混合H2/H∞鲁棒控制方法.首先借助于仿射二次稳定理论将整个多胞型不确定集合的稳定性问题转化为该集合各顶点的稳定性问题.利用参数依赖Lyapunov方法,给出了一个保证系统鲁棒稳定,并满足混合H2/H∞性能指标的充分条件.随后采用DILMI算法实现了Lyapunov变量和控制增益的解耦,无需引入附加变量就能够求解充分条件中的非凸优化问题.最后,关于F-16多胞型模型的飞行仿真验证了该方法的有效性.     

Robust H∞ control for linear systems withnorm-bounded time-varying uncertainty

Robust H_∞ control design for linear systems with uncertainty in both the state and input matrices is treated. A state feedback control design which stabilizes the plant and guarantees an H_∞-norm bound constraint on disturbance attenuation for all admissible uncertainties is presented. The robust H_∞ control problem is solved via the notion of quadratic stabilization with an H_∞ -norm bound. Necessary and sufficient conditions for quadratic stabilization with an H_∞-norm bound are derived. The results can be regarded as extensions of existing results on H_∞ control and robust stabilization of uncertain linear systems     

Affine parameter-dependent Lyapunov functions and real parametricuncertainty

This paper presents new tests to analyze the robust stability and/or performance of linear systems with uncertain real parameters. These tests are extensions of the notions of quadratic stability and performance where the fixed quadratic Lyapunov function is replaced by a Lyapunov function with affine dependence on the uncertain parameters. Admittedly with some conservatism, the construction of such parameter-dependent Lyapunov functions can be reduced to a linear matrix inequality (LMI) problem and hence is numerically tractable. These LMI-based tests are applicable to constant or time-varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations. They also avoid the frequency sweep needed in real-μ analysis, and numerical experiments indicate that they often compare favorably with μ analysis for time-invariant parameter uncertainty