Linear matrix inequality tests for synchrony of diffusively coupled nonlinear systems

2010 ◽  
Author(s):  
Murat Arcak
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Linear Matrix ◽  
Matrix Inequality

Linear Matrix Inequality Based Fractional Integral Sliding-Mode Control of Uncertain Fractional-Order Nonlinear Systems

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
Sara Dadras ◽  
Soodeh Dadras ◽  
HamidReza Momeni
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Sliding Mode ◽  
Superior Performance ◽  
Linear Matrix ◽  
Sliding Mode Controller ◽  
Matrix Inequality ◽  
Sliding Surface ◽  
Switching Law

A design of linear matrix inequality (LMI)-based fractional-order surface for sliding-mode controller of a class of uncertain fractional-order nonlinear systems (FO-NSs) is proposed in this paper. A new switching law is achieved guaranteeing the reachability condition. This control law is established to obtain a sliding-mode controller (SMC) capable of deriving the state trajectories onto the fractional-order integral switching surface and maintain the sliding motion. Using LMIs, a sufficient condition for existence of the sliding surface is derived which ensures the t−α asymptotical stability on the sliding surface. Through a numerical example, the superior performance of the new fractional-order sliding mode controller is illustrated in comparison with a previously proposed method.

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.

scholarly journals Robust DistributedH∞Filtering for Nonlinear Systems with Sensor Saturations and Fractional Uncertainties with Digital Simulation

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Dong Liu ◽  
Guangfu Tang ◽  
Zhiyuan He ◽  
Yan Zhao ◽  
Hui Pang
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Digital Simulation ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Parameter Uncertainties ◽  
Error System ◽  
Filtering Problem ◽  
Fractional Parameter

This paper is concerned with the robust distributedH∞filtering problem for nonlinear systems subject to sensor saturations and fractional parameter uncertainties. A sufficient condition is derived for the filtering error system to reach the requiredH∞performance in terms of recursive linear matrix inequality method. An iterative algorithm is then proposed to obtain the filter parameters recursively by solving the corresponding linear matrix inequality. A numerical example is presented to show the effectiveness of the proposed method.

New results on observer-based robust preview tracking control for Lipschitz nonlinear systems

2020 ◽  
pp. 107754632095365
Author(s):  
Xiao Yu ◽  
Fucheng Liao ◽  
Li Li
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Tracking Control ◽  
Reference Signal ◽  
State Feedback Control ◽  
Control Action ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Integral Control ◽  
Lipschitz Nonlinear Systems

In this article, the observer-based robust preview tracking control problem is revisited for discrete-time Lipschitz nonlinear systems. The proposed observer-based preview control scheme is composed of the integral control action, the observer-based state feedback control action, and the preview feedforward action of the reference signal. Sufficient design condition of controller and observer gains, which are able to ensure the simultaneously convergence of both the estimation error and the tracking error toward zero, is established in terms of linear matrix inequality by applying the Lyapunov function approach and several mathematical techniques. Compared with the existing result, the system model is more general, which could describe a larger range of practical processes. The observer-based preview controller design is simplified by computing the gain matrices of both observer and tracking controller simultaneously by only one-step linear matrix inequality procedure. Robustness against external disturbance is analyzed via the H∞ performance criterion to attenuate its effect on the performance signal. Finally, two numerical examples are provided to demonstrate the effectiveness of the suggested controller.

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.

scholarly journals A New Robust Training Law for Dynamic Neural Networks with External Disturbance: An LMI Approach

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Choon Ki Ahn
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Exponential Stability ◽  
External Disturbance ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Input Output ◽  
Lmi Approach ◽  
Dynamic Neural Networks ◽  
Numerical Examples

A new robust training law, which is called an input/output-to-state stable training law (IOSSTL), is proposed for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the IOSSTL is presented to not only guarantee exponential stability but also reduce the effect of an external disturbance. It is shown that the IOSSTL can be obtained by solving the LMI, which can be easily facilitated by using some standard numerical packages. Numerical examples are presented to demonstrate the validity of the proposed IOSSTL.

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