scholarly journals H∞Filtering for a Class of Piecewise Homogeneous Markovian Jump Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Yucai Ding ◽  
Hong Zhu ◽  
Shouming Zhong ◽  
Yuping Zhang ◽  
Yong Zeng
Keyword(s):  
Nonlinear Systems ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Attenuation Level ◽  
Stochastically Stable ◽  
Error System ◽  
Disturbance Attenuation Level ◽  
Filtering Problem

H∞filtering problem for a class of piecewise homogeneous Markovian jump nonlinear systems is investigated. The aim of this paper is to design a mode-dependent filter such that the filtering error system is stochastically stable and satisfies a prescribedH∞disturbance attenuation level. By using a new mode-dependent Lyapunov-Krasovskii functional, mixed mode-dependent sufficient conditions on stochastic stability are formulated in terms of linear matrix inequalities (LMIs). Based on this, the mode-dependent filter is obtained. A numerical example is given to illustrate the effectiveness of the proposed main results.

scholarly journals RobustH∞Filtering for Networked Control Systems with Random Sensor Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Shenping Xiao ◽  
Liyan Wang ◽  
Hongbing Zeng ◽  
Lingshuang Kong ◽  
Bin Qin
Keyword(s):  
Networked Control Systems ◽  
Filter Design ◽  
Design Method ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Attenuation Level ◽  
Exponentially Stable ◽  
Disturbance Attenuation Level ◽  
Filter Design Method

The robustH∞filtering problem for a class of network-based systems with random sensor delay is investigated. The sensor delay is supposed to be a stochastic variable satisfying Bernoulli binary distribution. Using the Lyapunov function and Wirtinger’s inequality approach, the sufficient conditions are derived to ensure that the filtering error systems are exponentially stable with a prescribedH∞disturbance attenuation level and the filter design method is proposed in terms of linear matrix inequalities. The effectiveness of the proposed method is illustrated by a numerical example.

scholarly journals H∞Filtering for Discrete-Time Genetic Regulatory Networks with Random Delay Described by a Markovian Chain

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yantao Wang ◽  
Xingming Zhou ◽  
Xian Zhang
Keyword(s):  
Regulatory Networks ◽  
External Disturbance ◽  
Measurement Data ◽  
Genetic Regulatory Networks ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Random Delay ◽  
Attenuation Level ◽  
Stochastically Stable ◽  
Disturbance Attenuation Level

This paper is concerned with theH∞filtering problem for a class of discretetime genetic regulatory networks with random delay and external disturbance. The aim is to designH∞filter to estimate the true concentrations of mRNAs and proteins based on available measurement data. By introducing an appropriate Lyapunov function, a sufficient condition is derived in terms of linear matrix inequalities (LMIs) which makes the filtering error system stochastically stable with a prescribedH∞disturbance attenuation level. The filter gains are given by solving the LMIs. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach; that is, our approach is available for a smallerH∞disturbance attenuation level than one in (Liu et al., 2012).

H∞ Filtering for Markov Jump Systems with Mixed Modes

2013 ◽  
Vol 706-708 ◽  
pp. 585-588
Author(s):  
Shu Lv ◽  
Shou Ming Zhong ◽  
Yu Cai Ding
Keyword(s):  
Stochastic Stability ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Attenuation Level ◽  
Stochastically Stable ◽  
Disturbance Attenuation Level ◽  
System Mode ◽  
Jump Systems

In this study, H_infinity filtering problem for a class of stochastic Markov jump systems is investigated. The system mode is assumed to be different from the delay mode. The aim of this paper is to design a mode-dependent filter such that the filtering error system is stochastically stable and satisfies a prescribed disturbance attenuation level. By using a mode-dependent Lyapunov functional, mixed mode-dependent sufficient condition on stochastic stability is formulated in terms of linear matrix inequalities. Based on the stochastic stability criterion, an H_infinity filter is developed.

scholarly journals Robust H∞ Filtering of Nonhomogeneous Markovian Jump Delay Systems via N-Step-Ahead Lyapunov-Krasovskii Functional Approach

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Jiwei Wen ◽  
Sing Kiong Nguang
Keyword(s):  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Parameter Uncertainties ◽  
Error System ◽  
Estimated Error ◽  
Markovian Jump Delay Systems ◽  
Filtering Problem

In this paper, we study the robust H∞ filtering problem for a class of nonhomogeneous Markovian jump delay systems (NMJDSs) with an N-step-ahead Lyapunov-Krasovskii functional (NALKF) approach. The N-step-ahead approach is utilized to reduce the conservatism of robust H∞ filtering. We aim to design filters such that, for all possible time-varying transition probabilities and all admissible parameter uncertainties and time-delays, the filtering error system is mean-square stable with a smaller estimated error and a lower dissipative level. In terms of linear matrix inequalities, sufficient conditions for the solvability of the addressed problem are developed via a moving horizon method. An illustrative example is included to elucidate advantages of the developed results and the practical potential of NALKF approach for NMJDSs.

scholarly journals Filtering-Based Fault Detection for Stochastic Markovian Jump System with Distributed Time-Varying Delays and Mixed Modes

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Yucai Ding ◽  
Hong Zhu ◽  
Shouming Zhong ◽  
Yuping Zhang ◽  
Jianwei Xia
Keyword(s):  
Fault Detection ◽  
Detection System ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jump ◽  
Stochastic Disturbance ◽  
Markovian Jump System ◽  
Stochastically Stable ◽  
Disturbance Attenuation Level

The problem of fault detection for stochastic Markovian jump system is considered. The system under consideration involves discrete and distributed time-varying delays, Itô-type stochastic disturbance, and different system and delay modes. The aim of this paper is to design a fault detection filter such that the fault detection system is stochastically stable and satisfies a prescribedH∞disturbance attenuation level. By using a novel Lyapunov functional, a mix-mode-dependent sufficient condition is formulated in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed main results.

scholarly journals NonlinearL2-Gain Analysis of Hybrid Systems in the Presence of Sliding Modes and Impacts

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
T. Osuna ◽  
O. E. Montano ◽  
Y. Orlov
Keyword(s):  
Sliding Mode ◽  
Numerical Study ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Sliding Modes ◽  
Time Dynamics ◽  
Attenuation Level ◽  
Disturbance Factor ◽  
Disturbance Attenuation Level ◽  
The Impact

TheL2-gain analysis is extended towards hybrid mechanical systems, operating under unilateral constraints and admitting both sliding modes and collision phenomena. Sufficient conditions for such a system to be internally asymptotically stable and to possessL2-gain less than ana priorigiven disturbance attenuation level are derived in terms of two independent inequalities which are imposed on continuous-time dynamics and on discrete disturbance factor that occurs at the collision time instants. The former inequality may be viewed as the Hamilton-Jacobi inequality for discontinuous vector fields, and it is separately specified beyond and along sliding modes, which occur in the system between collisions. Thus interpreted, the former inequality should impose the desired integral input-to-state stability (iISS) property on the Filippov dynamics between collisions whereas the latter inequality is invoked to ensure that the impact dynamics (when the state trajectory hits the unilateral constraint) are input-to-state stable (ISS). These inequalities, being coupled together, form the constructive procedure, effectiveness of which is supported by the numerical study made for an impacting double integrator, driven by a sliding mode controller. Desired disturbance attenuation level is shown to satisfactorily be achieved under external disturbances during the collision-free phase and in the presence of uncertainties in the transition phase.

scholarly journals Robust Finite-TimeH∞Control for Impulsive Switched Nonlinear Systems with State Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jian Guo ◽  
Chao Liu ◽  
Zhengrong Xiang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Switched Nonlinear Systems ◽  
State Delay ◽  
Impulsive Switched Systems ◽  
Finite Time Boundedness ◽  
Impulsive Switched System

This paper investigates robust finite-timeH∞control for a class of impulsive switched nonlinear systems with time-delay. Firstly, using piecewise Lyapunov function, sufficient conditions ensuring finite-time boundedness of the impulsive switched system are derived. Then, finite-timeH∞performance analysis for impulsive switched systems is developed, and a robust finite-timeH∞state feedback controller is proposed to guarantee that the resulting closed-loop system is finite-time bounded withH∞disturbance attenuation. All the results are given in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed method.

scholarly journals Stability Analysis and Robust H∞ Filtering for Discrete-time Nonlinear Systems with Time-varying Delays

2021 ◽  
Vol 20 ◽  
pp. 281-288
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Error System ◽  
Error Dynamics

In this paper, we investigate the problem of robust H∞ filter design for a class of discrete-time nonlinear systems. The systems under consider involves time-varying delays and parameters uncertainties. The main objective is to design a linear full-order filter to ensure that the resulting filtering error system is asymptotically stable with a prescribed H∞ performance level. By constructing an appropriate Lyapunov-Krasovskii functional, some novel sufficient conditions are established to guarantee the filter error dynamics system is robust asymptotically stable with H∞ performance γ , and the H∞ filter is designed in term of linear matrix inequalities. Finally, a numerical example is provided to illustrate the efficiency of proposed method.

Event-based switching control for production inventory systems with time-varying delays

2019 ◽  
Vol 42 (9) ◽  
pp. 1585-1593
Author(s):  
Chen-Yu Wu
Keyword(s):  
Raw Materials ◽  
Sufficient Conditions ◽  
Switching Control ◽  
Inventory Systems ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Time Varying ◽  
Production Inventory ◽  
Disturbance Attenuation Level ◽  
Event Based

This paper investigates event-based switching control for production inventory systems with time-varying delays. The different subsystems are established to describe the fact that the different production rates are adjusted to meet the different customer needs, and the conditions of average dwelling time are used to constrain the switchings. The event-triggered scheme, where the event generates when the relative error between the current review-data and the last transmission review-data exceeds a certain threshold, depicts the transmission of raw materials (or finished products) in practice. Then, the sufficient conditions of exponentially stable with a prescribed disturbance attenuation level [Formula: see text] and controller synthesis are formulated as linear matrix inequalitiess for the production inventory switching systems. A numerical example is presented to illustrate the effectiveness of the proposed method.

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