Variance-constrained filtering for uncertain stochastic systems with missing measurements

In this note, we consider a new filtering problem for linear uncertain discrete-time stochastic systems with missing measurements. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The system measurements may be unavailable (i.e., missing data) at any sample time, and the probability of the occurrence of missing data is assumed to be known. The purpose of this problem is to design a linear filter such that, for all admissible parameter uncertainties and all possible incomplete observations, the error state of the filtering process is mean square bounded, and the steady-state variance of the estimation error of each state is not more than the individual prescribed upper bound. It is shown that, the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic Riccati-like inequalities or linear matrix inequalities. The explicit expression of the desired robust filters is parameterized, and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach.     

Robust H∞ Control With Missing Measurements and Time Delays

In this technical note, the robust control problem is investigated for a class of stochastic uncertain discrete time-delay systems with missing measurements. The parameter uncertainties enter into the state matrices, and the missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. The purpose of the problem is to design a full-order dynamic feedback controller such that, for all possible missing observations and admissible parameter uncertainties, the closed-loop system is asymptotically mean-square stable and satisfies the prescribed performance constraint. Delay-dependent conditions are derived under which the desired solution exists, and the controller parameters are designed by solving a linear matrix inequality (LMI). A numerical example is provided to illustrate the usefulness of the proposed design method.     

State Estimation for Coupled Uncertain Stochastic Networks With Missing Measurements and Time-Varying Delays: The Discrete-Time Case

This paper is concerned with the problem of state estimation for a class of discrete-time coupled uncertain stochastic complex networks with missing measurements and time-varying delay. The parameter uncertainties are assumed to be norm-bounded and enter into both the network state and the network output. The stochastic Brownian motions affect not only the coupling term of the network but also the overall network dynamics. The nonlinear terms that satisfy the usual Lipschitz conditions exist in both the state and measurement equations. Through available output measurements described by a binary switching sequence that obeys a conditional probability distribution, we aim to design a state estimator to estimate the network states such that, for all admissible parameter uncertainties and time-varying delays, the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square. By employing the Lyapunov functional method combined with the stochastic analysis approach, several delay-dependent criteria are established that ensure the existence of the desired estimator gains, and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities (LMIs). Two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes.     

Robust State Estimation for Delayed Complex-Valued Neural Networks

This paper is concerned with the state estimation problem for the uncertain complex-valued neural networks with time delays. The parameter uncertainties are assumed to be norm-bounded. Through available output measurements containing nonlinear Lipschitz-like terms, we aim to design a state estimator to estimate the complex-valued network such that, for all admissible parameter uncertainties and time delay, the dynamics of the error-state system is guaranteed to be globally asymptotically stable. In addition, the case that there are no parameter uncertainties is also considered. By utilizing the Lyapunov functional method and matrix inequality techniques, some sufficient delay-dependent criteria are derived to assure the existence of the desired estimator gains. Finally, two numerical examples with simulations are presented to demonstrate the effectiveness of the proposed estimation schemes.     

Robust H-infinity filtering for time-delay systems with missing measurements: a parameter-dependent approach

Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytope and the missing measurements are described by a binary switching sequence satisfying a Bernoulli distribution. Our attention is focused on the analysis and design of robust H-infinity filters such that, for all admissible parameter uncertainties and all possible missing measurements, the filtering error system is exponentially mean-square stable with a prescribed H-infinity disturbance attenuation level. A parameter-dependent approach is proposed to derive a less conservative result. Sufficient conditions are established for the existence of the desired filter in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of the desired filter is also provided. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method. Robust H-infinity filtering; Polytopic uncertainties; Missing measurements; Time-delays; Parameter dependent; Linear matrix inequalities (LMIs)     

Robust H-infinity filtering for time-delay systems with missing measurements： a parameter-dependent approach

Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytope and the missing measurements are described by a binary switching sequence satisfying a Bernoulli distribution. Our attention is focused on the analysis and design of robust H-infinity filters such that, for all admissible parameter uncertainties and all possible missing measurements, the filtering error system is exponentially mean-square stable with a prescribed H-infinity disturbance attenuation level. A parameter-dependent approach is proposed to derive a less conservative result. Sufficient conditions are established for the existence of the desired filter in terms of certain linear matrix inequalities （LMIs）. When these LMIs are feasible, an explicit expression of the desired filter is also provided. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.     

Fault Detection for Fuzzy Systems With Intermittent Measurements

This paper investigates the problem of fault detection for Takagi-Sugeno (T-S) fuzzy systems with intermittent measurements. The communication links between the plant and the fault detection filter are assumed to be imperfect (i.e., data packet dropouts occur intermittently, which appear typically in a network environment), and a stochastic variable satisfying the Bernoulli random binary distribution is utilized to model the unreliable communication links. The aim is to design a fuzzy fault detection filter such that, for all data missing conditions, the residual system is stochastically stable and preserves a guaranteed performance. The problem is solved through a basis-dependent Lyapunov function method, which is less conservative than the quadratic approach. The results are also extended to T--S fuzzy systems with time-varying parameter uncertainties. All the results are formulated in the form of linear matrix inequalities, which can be readily solved via standard numerical software. Two examples are provided to illustrate the usefulness and applicability of the developed theoretical results.     

Robust fault detection for networked systems with communication delay and data missing

In this paper, the robust fault detection problem is investigated for a class of discrete-time networked systems with unknown input and multiple state delays. A novel measurement model is utilized to represent both the random measurement delays and the stochastic data missing phenomenon, which typically result from the limited capacity of the communication networks. The network status is assumed to vary in a Markovian fashion and its transition probability matrix is uncertain but resides in a known convex set of a polytopic type. The main purpose of this paper is to design a robust fault detection filter such that, for all unknown inputs, possible parameter uncertainties and incomplete measurements, the error between the residual signal and the fault signal is made as small as possible. By casting the addressed robust fault detection problem into an auxiliary robust H_∞ filtering problem of a certain Markovian jumping system, a sufficient condition for the existence of the desired robust fault detection filter is established in terms of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness and applicability of the proposed technique.     

Nonlinear observers for a class of continuous-time uncertain state delayed systems

This paper is concerned with the problem of observer design for a class of time-delay nonlinear systems with parameter uncertainties. The purpose of this problem is to design the gain-scheduled state observers such that, for the addressed nonlinearities as well as all admissible parameter uncertainties in state and output equations, the observation process remains globally exponentially stable, independently of the time delay. The nonlinearities are assumed to satisfy the global L ipschitz conditions, and the parameter uncertainties are allowed to be time varying, unstructured and norm bounded. An effective matrix inequality methodology is developed to solve the proposed problem. W e derive the conditions for the existence of the desired robust nonlinear observers, and then characterize the analytical expression of these observers. Two numerical examples demonstrate the validity and applicability of the present approach.     

State estimation for complex systems with randomly occurring nonlinearities and randomly missing measurements

This paper is concerned with the state estimation problem for the complex networked systems with randomly occurring nonlinearities and randomly missing measurements. The nonlinearities are included to describe the phenomena of nonlinear disturbances which exist in the network and may occur in a probabilistic way. Considering the fact that probabilistic data missing may occur in the process of information transmission, we introduce the randomly data missing into the sensor measurements. The aim of this paper is to design a state estimator to estimate the true states of the considered complex network through the available output measurements. By using a Lyapunov functional and some stochastic analysis techniques, sufficient criteria are obtained in the form of linear matrix inequalities under which the estimation error dynamics is globally asymptotically stable in the mean square. Furthermore, the state estimator gain is also obtained. Finally, a numerical example is employed to illustrate the effectiveness of the proposed state estimation conditions.     

ROBUST Hinfinity CONTROL FOR SYSTEMS WITH TIME-VARYING PARAMETER UNCERTAINTY AND VARIANCE CONSTRAINTS

In this paper, the problem of designing robust Hinfinity controllers for linear continuous-time systems subjected to time-varying parameter uncertainty and steady-state variance constraints is considered. The goal of this problem is to design the state feedback controller, such that for all admissible time-varying parameter perturbations, the steady-state variance of each state is not more than the individual prespecified upper bound and the Hinfinity norm of the transfer function from disturbance inputs to system outputs meets the prespecified upper bound constraint, simultaneously. The parameter uncertainties are allowed to be time-varying and norm-bounded. A purely algebraic matrix equation approach is effectively utilized to solve the problem addressed. The existence conditions as well as the explicit expression of desired controllers are presented, and two illustrative examples are used to demonstrate the applicability of the proposed design procedure.     

Dissipative control for state-saturated discrete time-varying systems with randomly occurring nonlinearities and missing measurements

In this paper, the dissipative control problem is investigated for a class of discrete time-varying systems with simultaneous presence of state saturations, randomly occurring nonlinearities as well as multiple missing measurements. In order to render more practical significance of the system model, some Bernoulli distributed white sequences with known conditional probabilities are adopted to describe the phenomena of the randomly occurring nonlinearities and the multiple missing measurements. The purpose of the addressed problem is to design a time-varying output-feedback controller such that the dissipativity performance index is guaranteed over a given finite-horizon. By introducing a free matrix with its infinity norm less than or equal to 1, the system state is bounded by a convex hull so that some sufficient conditions can be obtained in the form of recursive nonlinear matrix inequalities. A novel controller design algorithm is then developed to deal with the recursive nonlinear matrix inequalities. Furthermore, the obtained results are extended to the case when the state saturation is partial. Two numerical simulation examples are provided to demonstrate the effectiveness and applicability of the proposed controller design approach.     

测量数据丢失的随机不确定离散系统的鲁棒H2状态估计

由于频宽有限,或者传感器临时损坏,测量数据在网络中传输时可能会丢失.本文对一类测量数据丢失的不确定离散系统,研究了鲁棒H2状态估计问题.所有的系统矩阵的参数都属丁二给定的凸多面体区域.测量数据的丢失是随机发生的,认为它是已知概率的Bernoulli随机序列.对于所有容许的不确定和可能的数据丢失,采用线性矩阵不等式方法,给出了全阶和降阶的H2滤波器存在的充分条件.数值仿真表明本文所提方法的有效性.     

Reliable stabilization of stochastic time-delay systems with nonlinear disturbances

This paper is concerned with the stabilization problem for a class of continuous stochastic time-delay systems with nonlinear disturbances, parameter uncertainties and possible actuator failures. Both the stability analysis and synthesis problems are considered. The purpose of the stability analysis problem is to derive easy-to-test conditions for the uncertain nonlinear time-delay systems to be stochastically, exponentially stable. The synthesis problem, on the other hand, aims to design state feedback controllers such that the closed-loop system is exponentially stable in the mean square for all admissible uncertainties, nonlinearities, time-delays and possible actuator failures. It is shown that the addressed problem can be solved in terms of the positive definite solutions to certain algebraic matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the proposed design method.     

On stabilization of bilinear uncertain time-delay stochasticsystems with Markovian jumping parameters

In this paper, we investigate the stochastic stabilization problem for a class of bilinear continuous time-delay uncertain systems with Markovian jumping parameters. Specifically, the stochastic bilinear jump system under study involves unknown state time-delay, parameter uncertainties, and unknown nonlinear deterministic disturbances. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process. The whole system may be regarded as a stochastic bilinear hybrid system that includes both time-evolving and event-driven mechanisms. Our attention is focused on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are established to guarantee the existence of desired robust controllers, which are given in terms of the solutions to a set of either linear matrix inequalities (LMIs), or coupled quadratic matrix inequalities. The developed theory is illustrated by numerical simulation     

Quantized H∞ control for a class of 2-D systems with missing measurements

In this paper, the problem of quantized H∞ control is investigated for a class of 2-D systems described by Roesser model with missing measurements. The measurement missing of system state is described by a sequence of random variables obeying the Bernoulli distribution. Meanwhile, the state measurements are quantized by logarithmic quantizer before being communicated. By introducing a new 2-D Lyapunov-like function, a sufficient condition is derived to guarantee stochastically stable and H∞ performance of the closed-loop 2-D system, where the method of sector-bounded uncertainties is utilized to deal with quantization error. Based on the condition, the quantized H∞ control can be designed by using linear matrix inequality technique. A simulation example is also given to illustrate the proposed method.

     

Robust stabilization for generalized state-space systems with uncertainty

This paper is concerned with the problem of robust stabilization for generalized state-space systems with parameter uncertainty. The parameter uncertainty under consideration is time-invariant and unknown, but is norm-bounded. The problem we address is to design a state feedback controller such that the resulting closed-loop system is regular, impulsefree and stable for all admissible uncertainties. Via the notion of 'stabilizability and impulse eliminatibility' the robust stabilization problem is solved. Necessary and sufficient conditions for stabilizability and impulse eliminatibility are derived. When these conditions are satisfied, the desired stabilization state feedback controller can be constructed through finding parameters satisfying a certain matrix equation. Finally, an illustrative example is given to show the feasibility of the proposed technique.     

Robust H2/H∞-state estimation fordiscrete-time systems with error variance constraints

This paper studies the problem of an H_∞-norm and variance-constrained state estimator design for uncertain linear discrete-time systems. The system under consideration is subjected to time-invariant norm-bounded parameter uncertainties in both the state and measurement matrices. The problem addressed is the design of a gain-scheduled linear state estimator such that, for all admissible measurable uncertainties, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H_∞-norm upper bound constraint, simultaneously. The conditions for the existence of desired estimators are obtained in terms of matrix inequalities, and the explicit expression of these estimators is also derived. A numerical example is provided to demonstrate various aspects of theoretical results     

Robust H ∞ filtering for networked systems with multiple state delays

In this paper, a new robust H _∞ filter design problem is studied for a class of networked systems with multiple state-delays. Two kinds of incomplete measurements, namely, measurements with random delays and measurements with stochastic missing phenomenon, are simultaneously considered. Such incomplete measurements are induced by the limited bandwidth of communication networks, and are modelled as a linear function of a certain set of indicator functions that depend on the same stochastic variable. Attention is focused on the analysis and design problems of a full-order robust H _∞ filter such that, for all admissible parameter uncertainties and all possible incomplete measurements, the filtering error dynamics is exponentially mean-square stable and a prescribed H _∞ attenuation level is guaranteed. Some recently reported methodologies, such as delay-dependent and parameter-dependent stability analysis approaches, are employed to obtain less conservative results. Sufficient conditions, which are dependent on the occurrence probability of both the random sensor delay and missing measurement, are established for the existence of the desired filters in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of the desired filter can also be characterized. Finally, numerical examples are given to illustrate the effectiveness and applicability of the proposed design method.