$$H_{\infty } $$ H ∞ Filtering

This paper is concerned with the problem of Hinfin filtering for a class of linear systems with Markovian jump parameters and mode-dependent time-varying delays. The Lyapunov-Krasovskii method is used to derive a new delay-dependent Bounded Real Lemma (BRL) incorporating with an integral inequality, which guarantees that the filtering error system is not only exponentially stable in the mean square sense and with a guaranteed level of Hinfin noise attenuation as well. Then, some delay-dependent sufficient conditions for the existence of a suitable Markovian jump linear filter are established based on a set of strict linear matrix inequalities (LMIs). Some examples are given to show the effectiveness of the proposed method in this paper.

An iterative LMI approach for H∞ synthesis of multivariable PI/PD controllers for stable and unstable processes

In this paper, a novel delay‐dependent bounded real criterion and an improved sufficient condition are derived for the design of an H∞ state‐feedback controller for linear neutral time‐delay systems. On the basis of an augmented Lyapunov‐Krasovskii functional, a new bounded real lemma is introduced in terms of a convex linear matrix inequality (LMI) condition that can be solved using interior point algorithms. The bounded real lemma is extended to obtain a sufficient condition for the existence of a delay‐dependent H∞ memoryless state‐feedback controller. Neither any model transformation nor bounding of any of the cross terms are utilized while deriving the bounded real lemma. Moreover, the use of any free slack matrix variable approach is avoided to a certain extent in order not to increase the complexity of the synthesis problem. A cone complementary nonlinear minimization algorithm is employed to achieve a feasible solution set for the synthesis conditions. Finally, seven numerical examples are given to illustrate the effectiveness of the proposed method.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Robust reliable control in vibration suppression of sandwich circular plates

This correspondence is concerned with network-based H∞ filtering for discrete-time systems. The output signals of the system under consideration are transmitted to the filter through a constraint communication network, which usually leads to network-induced delays and packet dropouts. By introducing a logic data packet processor to choose the newest data signal from the network to actuate the filter, network-induced delays and packet dropouts are modeled as a Markov chain taking values in a finite set. As a result, the filter to be designed is modeled as a Markov jumping linear filter. By introducing some slack matrix variables in terms of prob ability identity, a less conservative bounded real lemma (BRL) is derived to ensure that the filtering error system is stochastically stable with a pre scribed H∞ level. Based on this BRL, suitable H∞ filters are designed by employing a cone complementary approach. A practical example on the Leslie model about some certain pest's structured population dynamics is given to show the effectiveness of the proposed approach.

H∞ control of singular time-delay systems via discretized Lyapunov functional

The aim of this paper is to analyse the problem of robust non-fragile H∞ controller for the combustion process in liquid propellant rocket motors chamber. Based on the delay decomposition approach, the whole delay interval is divided into two equidistant subintervals and a new Lyapunov-Krasovskii functional (LKF) which contains some triple-integral terms and augment terms is introduced on each interval. By using L-K stability theorem, integral inequality method together with free weighting matrix approach, a new delay-dependent bounded real lemma (BRL) is formulated. Then, by applying the BRL, non-fragile H∞ controller is formulated in terms of linear matrix inequalities (LMI), where no any parameter needs to be turned and apt to realisation. Finally, simulation results are given to illustrate that the designed controller has good robust and non-fragile performance.

A Delay Decomposition Approach to H∞ Control of Networked Control Systems

Improved delay-dependent bounded real lemma for uncertain time-delay systems

This paper is concerned with the distributed model predictive control (MPC) problem for a class of discrete-time Markovian jump linear systems (MJLSs) subject to actuator saturation and polytopic uncertainty in system matrices. The global system is decomposed into several subsystems which coordinate with each other. A set of distributed controllers is designed by solving a min-max optimization problem in terms of the solutions of linear matrix inequalities (LMIs). An iterative algorithm is developed to achieve the online computation. Finally, a simulation example is employed to show the effectiveness of the proposed algorithm.

This paper presents a new dilated linear matrix inequality (LMI) representation to design a state feedback controller and a dynamic feedforward disturbance compensator for linear parameter-varying (LPV) systems. The improved LMIs are convex and finite-dimensional without any iterative approach. The designs are based on a new proposed equivalent bounded real lemma (BRL) by means of matrix dilation for LPV systems and uncertain linear systems under time-varying parametric uncertainties (TVPUs). This dilated BRL provides lower conservative results than existing methods in terms of robust stability. Accordingly, a dynamic disturbance compensator is designed in addition to a state feedback controller. This paper mainly focuses on the design of compensators against disturbances in addition to the design of state feedback controllers. The dynamic matrices of the compensator change with the time-varying parameters of the LPV or uncertain system during operation, assuming that the disturbances and the parameters are measurable or observable. The compensator can be designed to attenuate the disturbances/noises or to improve reference tracking. Finally, numerical and simulation outcomes are presented to prove both the effectiveness and lower conservativeness of the proposed LMIs.

Robust H∞ control for discrete-time fuzzy systems via basis-dependent Lyapunov functions

In this paper, the problem of simultaneous fault detection and control (SFDC) for linear switched systems in discrete- and continuous-time cases under a mixed H−/H∞ framework is considered. In essence, a single unit called detector/controller is designed, where the detector is an observer and the controller is an observer-based controller. The conventional mixed H−/H∞ problem is a conservative approach due to the selection of equal Lyapunov matrices. Extended linear matrix inequalities (LMIs) characterizations are used to reduce the conservativeness by the introduction of additional matrix variables, so as to eliminate the coupling of Lyapunov matrices with the system matrices. Indeed, the idea presented in this paper is based on the average dwell time (ADT) and conservatism reduction approaches, which lead to some sufficient conditions for solving the problem in terms of LMI feasibility conditions. Two examples are provided to demonstrate the effectiveness of the proposed method.

This paper is concerned with the problem of robust l2 - l∞ control for uncertain discrete-time switched systems with time delay in the state. The uncertainty is assumed to be of structured linear fractional form which includes the norm-bounded uncertainty as a special case. The control design approach is facilitated by introducing some additional instrumental matrix variables. The additional matrix variables decouple the Lyapunov and system matrices, which make the control design feasible. The proposed approach leads to less conservativeness of previous design methods, and the results also generalize earlier works for a more general parametric uncertainty structure. A numerical example is also given to demonstrate the effectiveness and the potential of the proposed techniques.

摘要: 针对一类具有非线性不确定离散非线性系统设计了可靠H∞滤波器. 设计的结果使得滤波误差系统在标称状态及具有传感器失效状态时不仅是渐进稳定的, 而且满足给定的H∞范数约束. 采用Lyapunov稳定性理论和线性矩阵不等式技术给出了滤波器存在的充分条件. 而且, 为了减少设计的保守性及得到更好的性能, 我们利用松弛变量来解耦Lyapunov矩阵及系统动态矩阵. 数值仿真例子说明设计方法的有效性. 关键词: H∞滤波 / 可靠滤波 / Lyapunov函数 / 传感器失效 / 线性矩阵不等式(LMI)