scholarly journals Estimation for Stochastic Nonlinear Systems with Randomly Distributed Time-Varying Delays and Missing Measurements

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yan Che ◽  
Huisheng Shu ◽  
Xiu Kan
Keyword(s):  
Nonlinear Systems ◽  
Estimation Error ◽  
Linear Matrix ◽  
Stochastic Nonlinear Systems ◽  
Time Varying ◽  
Matrix Inequality ◽  
Missing Measurements ◽  
Design Procedures ◽  
Mean Square Stability ◽  
The Mean

The estimation problem is investigated for a class of stochastic nonlinear systems with distributed time-varying delays and missing measurements. The considered distributed time-varying delays, stochastic nonlinearities, and missing measurements are modeled in random ways governed by Bernoulli stochastic variables. The discussed nonlinearities are expressed by the statistical means. By using the linear matrix inequality method, a sufficient condition is established to guarantee the mean-square stability of the estimation error, and then the estimator parameters are characterized by the solution to a set of LMIs. Finally, a simulation example is exploited to show the effectiveness of the proposed design procedures.

Robust integral-observer-based fault estimation for Lipschitz nonlinear systems with time-varying uncertainties

2018 ◽  
Vol 41 (7) ◽  
pp. 1965-1974 ◽  
Author(s):  
Ammar Zemzemi ◽  
Mohamed Kamel ◽  
Ahmed Toumi ◽  
Mondher Farza
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Estimation Error ◽  
Hybrid Approach ◽  
Disturbance Attenuation ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Sensor Fault

This paper addresses the problem of state estimation and sensor fault reconstruction conjointly for a class of nonlinear systems with time-varying uncertainties for which the nonlinear characteristic satisfies the Lipschitz circumstance. A hybrid approach based on an integral observer and sliding-mode theory has been proposed in order to model sensor fault as a virtual actuator one. For the augmented model, the observer matching condition is not satisfied. To overcome this problem, a new method, which improves the design approach and enhances the rapidity of the fault estimation convergence, has been proposed. The fault estimation error effect is minimized by integrating the [Formula: see text] disturbance attenuation level. The proposed design is formulated and derived as a linear matrix inequality problem. Parameters of this observer are calculated through the linear matrix inequality technique. The proposed method has been validated through an example of a single-link manipulator robot. Simulation results show that this approach can estimate the state and the sensor fault successfully, despite the time-varying uncertainties and the presence of unknown inputs.

A Novel Delay-Independent Robust Adaptive Controller Design for Uncertain Nonlinear Systems With Time-Varying State Delay

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Hadi Azmi ◽  
Alireza Yazdizadeh
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Closed Loop ◽  
Controller Design ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
System Delay ◽  
Closed Loop System

Abstract In this paper, two novel adaptive control strategies are presented based on the linear matrix inequality for nonlinear Lipschitz systems. The proposed approaches are developed by creatively using Krasovskii stability theory to compensate parametric uncertainty, unknown time-varying internal delay, and bounded matched or mismatched disturbance effects in closed-loop system of nonlinear systems. The online adaptive tuning controllers are designed such that reference input tracking and asymptotic stability of the closed-loop system are guaranteed. A novel structural algorithm is developed based on linear matrix inequality (LMI) and boundaries of the system delay or uncertainty. The capabilities of the proposed tracking and regulation methods are verified by simulation of three physical uncertain nonlinear system with real practical parameters subject to internal or state time delay and disturbance.

Stability and stabilization of 2-D Roesser systems with time-varying delays subject to missing measurements

2017 ◽  
Vol 40 (6) ◽  
pp. 1999-2010 ◽  
Author(s):  
Bu Xuhui ◽  
Tian Senping ◽  
Cui Lizhi ◽  
Yang Junqi
Keyword(s):  
Linear Matrix ◽  
Time Varying ◽  
Missing Measurements ◽  
Delayed System ◽  
Stability And Stabilization ◽  
The Mean ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Loop 2 ◽  
Robust Stability And Stabilization

This paper addresses the problem of stability and stabilization for a class of two-dimensional (2-D) Roesser systems with time-varying delays subject to missing measurements. The missing phenomenon of the sensor measurement is governed by a stochastic variable satisfying the Bernoulli random binary distribution. The aim of this paper is focused on the design of a state feedback controller such that the closed-loop 2-D system is asymptotic stability in the mean square sense. A delay-dependent stability condition is derived in terms of linear matrix inequalities, and formulas can be given for the control law design. Furthermore, the results are also extended to robust stability and stabilization of the uncertain 2-D time-varying delayed system. Numerical examples are given to illustrate the effectiveness of proposed approach.

Stability and Stabilization for Discrete System With Probabilistic Nonlinearities

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Xia Zhao ◽  
Engang Tian
Keyword(s):  
Sufficient Conditions ◽  
Discrete Systems ◽  
System Model ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Mean Square Stability ◽  
New Type ◽  
Stability And Stabilization ◽  
The Mean ◽  
Varying Delay

This paper investigates stability and stabilization of discrete systems with probabilistic nonlinearities and time-varying delay. New characters of the nonlinearities, the probability of the nonlinearities happening between different bounds, are used to build new type of system model, which can help us make a full use of the inner variation information of the nonlinearities. With the help of the new characters, new system model is proposed. Then, sufficient conditions for the mean square stability of the system can be obtained by using the Lyapunov functional approach and linear matrix inequalities technique. An example is proposed to illustrate the efficiency of the proposed method.

scholarly journals Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Qiankun Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Computationally Efficient ◽  
Inequality Technique ◽  
General Activation ◽  
Delay Dependent

The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

scholarly journals LMI-Based Approach for Exponential Robust Stability of High-Order Hopfield Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Yangfan Wang ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Robust Stability ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Global Exponential Robust Stability

This paper studies the problems of global exponential robust stability of high-order hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high-order neural networks are established, which are easily verifiable and have a wider adaptive.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

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