LMI OPTIMIZATION APPROACH FOR DELAY‐DEPENDENT H∞ CONTROL OF TIME‐VARYING DELAY SYSTEMS

In this paper, the robust delay‐dependent H_∞ control for a class of uncertain systems with time‐varying delay is considered. An improved state feedback H_∞ control is proposed to minimize the H_∞‐norm bound via the LMI optimization approach. Based on the proposed result, delay‐dependent criteria are obtained without using the model transformation technique or bounded inequalities on cross product terms. The linear matrix inequality (LMI) optimization approach is used to design the robust H_∞ state feedback control. Some numerical examples are given to illustrate the effectiveness of the approach.     

State‐saturated H∞ filtering with randomly occurring nonlinearities and packet dropouts: the finite‐horizon case

This paper deals with the H_∞ filtering problem for a class of discrete time‐varying systems with state saturations, randomly occurring nonlinearities as well as successive packet dropouts. Two mutually independent sequences of random variables that obey the Bernoulli distribution are employed to describe the random occurrence of the nonlinearities and packet dropouts. The purpose of the addressed problem is to design a time‐varying filter such that the H_∞ disturbance attenuation level is guaranteed, over a given finite‐horizon, for the filtering error dynamics in the presence of saturated states, randomly occurring nonlinearities, and successive packet dropouts. By introducing a free matrix with its infinity norm less than or equal to 1, the error state is bounded by a convex hull so that some sufficient conditions obtained via solving a certain set of recursive nonlinear matrix inequalities. Furthermore, the obtained results are extended to the case when state saturations are partial. Two numerical simulation examples are provided to demonstrate the effectiveness and applicability of the proposed filter design approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Nonlinear H∞ observer design for one‐sided Lipschitz discrete‐time singular systems with time‐varying delay

This paper investigates the H_∞ observer design problem for a class of nonlinear discrete‐time singular systems with time‐varying delays and disturbance inputs. The nonlinear systems can be rectangular and the nonlinearities satisfy the one‐sided Lipschitz condition and quadratically inner‐bounded condition, which are more general than the traditional Lipschitz condition. By appropriately dealing with these two conditions and applying several important inequalities, a linear matrix inequality–based approach for the nonlinear observer design is proposed. The resulting nonlinear H_∞ observer guarantees asymptotic stability of the estimation error dynamics with a prescribed performance γ. The synthesis condition of H_∞ observer design for nonlinear discrete‐time singular systems without time delays is also presented. The design is first addressed for one‐sided Lipschitz discrete‐time singular systems. Finally, two numerical examples are given to show the effectiveness of the present approach.     

Robust finite‐time H∞ synchronization for uncertain discrete‐time systems with nonhomogeneous Markovian jump: Observer‐based case

In this article, the problem of robust finite‐time H_∞ synchronization control is investigated for a class of uncertain discrete‐time master‐slave systems with Markovian switching parameters in the observer‐based case. Parameter uncertainties are assumed to be norm‐bounded, and the polyhedral character is utilized to describe the transition probabilities of nonhomogeneous Markov chain. By using stochastic Lyapunov function method and finite‐time analysis techniques, novel sufficient conditions that include the master‐slave parameters are obtained for designing an observer‐based finite‐time H_∞ synchronization control law in terms of linear matrix inequalities. The effectiveness of the proposed theoretical scheme is finally demonstrated by some simulations.     

H∞ Non‐Fragile Synchronous Guaranteed Control of Uncertainty Complex Dynamic Network with Time‐Varying Delay

A kind of H_∞ non‐fragile synchronization guaranteed control method is put forward for a class of uncertain time‐varying delay complex network systems with disturbance input. The network under consideration includes unknown but bounded nonlinear coupling functions f(x) and the coupling term and node system with time‐varying delays. The nonlinear vector function f(x) need not be differentiable but should satisfy the norm bound. A non‐fragile state feedback controller of the gain with sufficiently large regulation margin is designed. It is ensured that the parameters of the controller could still be effective under small perturbation. The sufficient conditions for the existence of H_∞ synchronous non‐fragile guaranteed control of this system have been obtained by constructing a suitable Lyapunov‐Krasovskii functional, adopting matrix analysis, using the theorem of Schur complement and linear matrix inequalities (LMI). These conditions can guarantee robust asymptotic stability for each node of network with disturbance as well as achieve a prescribed robust H_∞ performance level. Finally, the feasibility of the designed method is verified by a numerical example.     

H∞ filtering for uncertain time‐varying systems with multiple randomly occurred nonlinearities and successive packet dropouts

This paper is concerned with the robust H_∞ finite‐horizon filtering problem for discrete time‐varying stochastic systems with multiple randomly occurred sector‐nonlinearities (MROSNs) and successive packet dropouts. MROSNs are proposed to model a class of sector‐like nonlinearities that occur according to the multiple Bernoulli distributed white sequences with a known conditional probability. Different from traditional approaches, in this paper, a time‐varying filter is designed directly for the addressed system without resorting to the augmentation of system states and measurement, which helps reduce the filter order. A new H_∞ filtering technique is developed by means of a set of recursive linear matrix inequalities that depend on not only the current available state estimate but also the previous measurement, therefore ensuring a better accuracy. Finally, two illustrative examples are used to demonstrate the effectiveness and applicability of the proposed filter design scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

Finite‐Time H∞ Filtering for Nonlinear Continuous‐Time Singular Semi‐Markov Jump Systems

The stochastic finite‐time H_∞ filtering issue for a class of nonlinear continuous‐time singular semi‐Markov jump systems is discussed in this paper. Firstly, sufficient conditions on singular stochastic H_∞ finite‐time boundedness for the filtering error system are established. The existence of a unique solution for the corresponding system is also ensured. Secondly, based on the bounds of the time‐varying transition rate, without imposing constraints on slack variables, a novel approach to finite‐time H_∞ filter design is proposed in the forms of strict LMIs, which guarantees the filtering error system is singular stochastic H_∞ finite‐time bounded and of a unique solution. Compared with the existing ones, the presented results reveal less conservativeness. Finally, one numerical example is exploited to testify the advantage of the proposed design technique.     

H∞ Control of Linear Discrete‐Time Systems With Norm‐Bounded Nonlinear Uncertainties

In this paper, robust H_∞ control of a class of discrete‐time uncertain systems in state‐space form with linear nominal parts and norm‐bounded nonlinear uncertainties in both state and output equations is discussed. Such systems have a unique characterisic; that is, the two norm‐bounded nonlinear uncertainties have the equivalent representation by means of time‐varying and norm‐bounded linear uncertainties. To overcome the conservativenss of [5], the two nonlinear uncertainty sets are considered to be different. Then, by converting such systems into related discrete‐time linear systems with time‐varying and norm‐bounded linear uncertainties, we obtain that a sufficient condition for robust H_∞ control of such systems is equivalent to the solvability of the same problem of the related linear uncertain systems, which is solvable by means of a linear algebraic Riccati inequality.     

Delay‐range‐dependent H∞ control for Markovian jump systems with mode‐dependent time delays

This paper considers mean‐square exponential stability and H_∞ control problems for Markovian jump systems (MJSs) with time delays which are time‐varying in an interval and depend on system mode. By exploiting a novel Lyapunov‐Krasovskii functional which takes into account the range of delay, and by making use of some techniques, new delay‐range‐dependent stability result and bounded real lemma for MJSs are obtained, where the introduction of the lower bound of delay is shown to be advantageous for reducing conservatism. Moreover, a sufficient condition for the solvability of the H_∞ control problem is derived in terms of linear matrix inequalities. Finally, illustrative examples are presented to show the advantage and effectiveness of the proposed approaches. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Reliable H ∞ Filtering for Mixed Time‐Delay Systems with Stochastic Nonlinearities and Multiplicative Noises

This paper investigates the reliable H_∞ filtering problem for a class of mixed time‐delay systems with stochastic nonlinearities and multiplicative noises. The mixed delays comprise both discrete time‐varying and distributed delays. The stochastic nonlinearities in the form of statistical means cover several well‐studied nonlinear functions. The multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. Furthermore, the failures of sensors are quantified by a variable varying in a given interval. In the presence of mixed delays, stochastic nonlinearities, and multiplicative noises, sufficient conditions for the existence of a reliable H _∞ filter are derived, such that the filtering error dynamics is asymptotically mean‐square stable and also achieves a guaranteed H _∞ performance level. Then, a linear matrix inequality (LMI) approach for designing such a reliable H _∞ filter is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.     

L2‐Gain Analysis for Synchronization of Stochastic Complex Network with Switched Topology and Time‐Varying Delay

We investigate the exponential stability and L₂‐gain analysis for the synchronization of stochastic complex networks under average dwell time switched topology with consideration of external disturbance, internal noise and fast time‐varying delay in the synchronized process. Based on the proposed stochastic network, a new L₂‐gain synchronization is proposed to solve the mean‐square exponential stable under switched topology with an H_∞ performance from the extrinsic disturbances to the synchronization error. The obtained results are applicable for the fast time‐varying case with larger‐than‐1 delay derivative. Finally, numerical simulations are performed to demonstrate the effectiveness of our strategies.     

H∞ Control for Continuous‐Time Mean‐Field Stochastic Systems

An H_∞‐type control is considered for mean‐field stochastic differential equations (SDEs) in this paper. A stochastic bounded real lemma (SBRL) is proved for mean‐field stochastic continuous‐time systems with state‐ and disturbance‐dependent noise. Based on SBRL, a sufficient condition is given for the existence of a stabilizing H_∞ controller in terms of coupled nonlinear matrix inequalities.     

Elegant antidisturbance fault‐tolerant control for stochastic systems with multiple heterogeneous disturbances

In this article, the elegant antidisturbance fault‐tolerant control (EADFTC) problem is studied for a class of stochastic systems in the simultaneous presence of multiple heterogeneous disturbances and time‐varying faults. The multiple heterogeneous disturbances include white noise, norm bounded uncertain disturbances and uncertain modeled disturbances with multiple nonlinearities and unknown amplitudes, frequencies, and phases. The time‐varying fault signals are caused by lose efficacy of actuator. To online estimate uncertain modeled disturbances and time‐varying faults, a novel composite observer structure consisting of the adaptive nonlinear disturbance observer and the fault diagnosis observer is constructed. The novel EADFTC strategy is proposed by integrating composite observer structure with adaptive disturbance observer‐based control theory and H_∞ technology. It is proved that all the signals of closed‐loop system are asymptotically bounded in mean square under the circumstances of multiple heterogeneous disturbances and time‐varying faults occur simultaneously. Finally, the effectiveness and availability of proposed strategy are demonstrated by means of the numerical simulation and a doubly fed induction generators system simulation, respectively.     

H∞ filtering for singular systems with time‐varying delay

This paper is concerned with the delay‐dependent H_∞ filtering problem for singular systems with time‐varying delay in a range. In terms of linear matrix inequality approach, the delay‐range‐dependent bounded real lemmas are proposed, which guarantee the considered system to be regular, impulse free and exponentially stable while satisfying a prescribed H_∞ performance level. The sufficient conditions are proposed for the existence of linear H_∞ filter. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.     

LMI APPROACH TO ROBUST FILTERING FOR DISCRETE TIME‐DELAY SYSTEMS WITH NONLINEAR DISTURBANCES

This paper investigates the problem of robust filtering for a class of uncertain nonlinear discrete‐time systems with multiple state delays. It is assumed that the parameter uncertainties appearing in all the system matrices reside in a polytope, and that the nonlinearities entering into both the state and measurement equations satisfy global Lipschitz conditions. Attention is focused on the design of robust full‐order and reduced‐order filters guaranteeing a prescribed noise attenuation level in an H∞ or l₂‐l∞ sense with respect to all energy‐bounded noise disturbances for all admissible uncertainties and time delays. Both delay‐dependent and independent approaches are developed by using linear matrix inequality (LMI) techniques, which are applicable to systems either with or without a priori information on the size of delays.     

Robust H∞ Filtering For Uncertain Stochastic Time‐Delay Systems

This paper deals with the problem of robust H_∞ filtering for uncertain stochastic systems. The system under consideration is subject to time‐varying norm‐bounded parameter uncertainties and unknown time delays in both the state and measurement equations. The problem we address is the design of a stable filter that ensures the robust stochastic stability and a prescribed H_∞ performance level for the filtering error system irrespective of all admissible uncertainties and time delays. A suffient condition for the solvability of this problem is proposed and a linear matrix inequality approach is developed for the design of the robust H_∞ filters. An illustrative example is provided to demonstrate the effctiveness of the proposed approach.     

Finite‐horizon fault estimation under imperfect measurements and stochastic communication protocol: Dealing with finite‐time boundedness

In this paper, we analyze the finite‐horizon fault estimation issue for a kind of time‐varying nonlinear systems with imperfect measurement signals under the stochastic communication protocol (SCP). The imperfect measurements result from randomly occurring sensor nonlinearities obeying sensor‐wise Bernoulli distributions. The Markov‐chain‐driven SCP is introduced to regulate the signal transmission to alleviate the communication congestion. The aim of the considered issue is to propose the design algorithm of a group of time‐varying fault estimators such that the estimation error dynamics satisfies both the H_∞ and the finite‐time boundedness (FTB) performance requirements. First, sufficient conditions are set up to guarantee the existence of the satisfactory H_∞ FTB fault estimators through intensive stochastic analyses and matrix operations. Then, the gains of such fault estimators are explicitly parameterized by resorting to the solution to recursive linear matrix inequalities. Finally, the correctness of the devised fault estimation approach is demonstrated by a numerical example.     

A NEW INTEGRAL INEQUALITY APPROACH TO DELAY‐DEPENDENT ROBUST H∞ CONTROL

A design method for the robust H_∞ control of an uncertain linear system with a time‐varying state delay is proposed. First, an integral inequality that we recently obtained is employed to establish a new delay‐dependent bounded real lemma for a system with a time‐varying delay. The lemma uses neither a model transformation nor a bounding technique for cross terms. Then, the lemma is used in combination with a matrix decomposition method to derive delay‐dependent conditions for the existence of robust H_∞ control based on linear matrix inequalities. Finally, some numerical examples are given to demonstrate the validity of the method.     

ROBUST H∞ CONTROL AND QUADRATIC STABILIZATION OF DISCRETE‐TIME SWITCHED SYSTEMS WITH NORM‐BOUNDED TIME‐VARYING UNCERTAINTIES

We focus on robust H_∞ control analysis and synthesis for discretetime switched systems with norm‐bounded time‐varying uncertainties. Sufficient conditions are derived to guarantee quadratic stability along with a prescribed H_∞‐norm bound. Each of them can be dealt with as a linear matrix inequality (LMI) which can be tested with efficient algorithms. All the switching rules are constructively designed, and do not rely on any uncertainties.     

Quadratic stabilizability and H∞ control of linear discrete‐time stochastic uncertain systems

This paper considers quadratic stabilizability and H_∞ feedback control for stochastic discrete‐time uncertain systems with state‐ and control‐dependent noise. Specifically, the uncertain parameters considered are norm‐bounded and external disturbance is an l²‐square summable stochastic process. Firstly, both quadratic stability and quadratic stabilization criteria are presented in the form of linear matrix inequalities (LMIs). Then we design the robust H_∞ state and output feedback H_∞ controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H_∞ controllable. Sufficient conditions for the existence of the desired robust H_∞ controllers are obtained via LMIs. Finally, some examples are supplied to illustrate the effectiveness of our results.