LMI Enhanced Observer Design for Lipschitz Nonlinear Systems

2013 ◽  
Vol 756-759 ◽  
pp. 420-424
Author(s):  
Feng Qiao ◽  
Qing Ma ◽  
Feng Zhang ◽  
Hao Ming Zhao
Keyword(s):  
Nonlinear Systems ◽  
Observer Design ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Simulation Studies ◽  
Complex Issue ◽  
Lipschitz Nonlinear Systems ◽  
Satisfy Lipschitz Condition ◽  
The Relationship ◽  
Selection Of

Observer design for nonlinear systems has been an important and complex issue for decades. In this paper, considering a class of nonlinear systems which satisfy Lipschitz condition, a method for observer design is investigated based on Linear Matrix Inequality (LMI). This study focuses on the selection of gain matrices using LMI for two kinds of Lipschitz nonlinear systems, which are classified by the relationship between output and state. Simulation studies are made with Matlab/Simulink in this paper, and the simulation results verify the effectiveness of the proposed method.

Observer Design for Lipschitz Nonlinear Systems with Output Uncertainty

2014 ◽  
Vol 533 ◽  
pp. 277-280
Author(s):  
Wei Zou ◽  
Yu Sheng Liu ◽  
Kai Liu
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Lyapunov Method ◽  
Observer Design ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Output Uncertainty ◽  
Lipschitz Nonlinear Systems ◽  
Simulation Results

This paper presents an observer design for Lipschitz nonlinear systems with output uncertainty. By means of Lyapunov method as well as linear matrix inequality (LMI), the observer gain matrix is determined and a sufficient condition ensuring the asymptotic stability of the observer is proposed. Simulation results demonstrate the robustness of the proposed observer for output uncertainty.

scholarly journals Observer Design for One-Sided Lipschitz Nonlinear Systems Subject to Measurement Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Sohaira Ahmad ◽  
Raafia Majeed ◽  
Keum-Shik Hong ◽  
Muhammad Rehan
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Time Lag ◽  
Time Derivative ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Linear Matrix ◽  
Lipschitz Nonlinear Systems ◽  
System States ◽  
Lipschitz Systems

This paper presents a novel nonlinear observer-design approach to one-sided Lipschitz nonlinear systems in the presence of output delays. The crux of the approach is to overcome the practical consequences of time delays, encountered due to distant sensor position and time lag in measurement, for estimation of physical and engineering nonlinear system states. A Lyapunov-Krasovskii functional is employed, the time derivative of which is solved using Jensen’s inequality, one-sided Lipschitz condition, and quadratic inner-boundedness, and, accordingly, design conditions for delay-range-dependent nonlinear observer for delayed one-sided Lipschitz systems are derived. Further, novel solutions to the problems of delay-dependent observer synthesis of one-sided Lipschitz models and delay-range-dependent state estimation of linear and Lipschitz nonlinear systems are deduced from the present delay-range-dependent technique. An observer formulation methodology for retrieval of one-sided Lipschitz nonlinear-system states, which is robust againstL2norm-bounded perturbations, is devised. The resultant design conditions, in contrast to the conventional procedures, can be solved via less conservative linear matrix inequality- (LMI-) based routines that succeed by virtue of additional LMI variables, meaningful transformations, and cone complementary linearization algorithm. Numerical examples are worked out to illustrate the effectiveness of the proposed observer-synthesis approach for delayed one-sided Lipschitz systems.

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.

scholarly journals Adaptive observer-based fault estimation for a class of Lipschitz nonlinear systems

2016 ◽  
Vol 26 (2) ◽  
pp. 245-259 ◽  
Author(s):  
Nabil Oucief ◽  
Mohamed Tadjine ◽  
Salim Labiod
Keyword(s):  
Nonlinear Systems ◽  
Transfer Functions ◽  
Matching Condition ◽  
Observer Design ◽  
Joint Estimation ◽  
Adaptive Observer ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Lipschitz Nonlinear Systems ◽  
Observer Matching Condition

Abstract Fault input channels represent a major challenge for observer design for fault estimation. Most works in this field assume that faults enter in such a way that the transfer functions between these faults and a number of measured outputs are strictly positive real (SPR), that is, the observer matching condition is satisfied. This paper presents a systematic approach to adaptive observer design for joint estimation of the state and faults when the SPR requirement is not verified. The proposed method deals with a class of Lipschitz nonlinear systems subjected to piecewise constant multiplicative faults. The novelty of the proposed approach is that it uses a rank condition similar to the observer matching condition to construct the adaptation law used to obtain fault estimates. The problem of finding the adaptive observer matrices is formulated as a Linear Matrix Inequality (LMI) optimization problem. The proposed scheme is tested on the nonlinear model of a single link flexible joint robot system.

scholarly journals Robust Observer Design for Switched Positive Linear System with Uncertainties

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yanke Zhong ◽  
Tefang Chen
Keyword(s):  
Linear System ◽  
Linear Matrix Inequality ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Observer Design ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Robust Observer ◽  
Slack Variable

This paper is concerned with the design of a robust observer for the switched positive linear system with uncertainties. Sufficient conditions of building a robust observer are established by using the multiple copositive Lyapunov-krasovskii function and the average dwell time approach. By introducing an auxiliary slack variable, these sufficient conditions are transformed into LMI (linear matrix inequality). A numerical example is given to illustrate the validities of obtained results.

Unknown input fractional-order functional observer design for one-side Lipschitz time-delay fractional-order systems

2019 ◽  
Vol 41 (15) ◽  
pp. 4311-4321 ◽  
Author(s):  
Mai Viet Thuan ◽  
Dinh Cong Huong ◽  
Nguyen Huu Sau ◽  
Quan Thai Ha
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Quadratic Function ◽  
Observer Design ◽  
Linear Matrix ◽  
Unknown Input ◽  
Functional Observer ◽  
The One

This paper addresses the problem of unknown input fractional-order functional state observer design for a class of fractional-order time-delay nonlinear systems. The nonlinearities consist of two parts where one part is assumed to satisfy both the one-sided Lipschitz condition and the quadratically inner-bounded condition and the other is not necessary to be Lipschitz and can be regarded as an unknown input, making the wider class of considered nonlinear systems. By taking the advantages of recent results on Caputo fractional derivative of a quadratic function, we derive new sufficient conditions with the form of linear matrix inequalities (LMIs) to guarantee the asymptotic stability of the systems. Four examples are also provided to show the effectiveness and applicability of the proposed method.

scholarly journals Robust Preview Control for a Class of Uncertain Discrete-Time Lipschitz Nonlinear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Xiao Yu ◽  
Fucheng Liao ◽  
Jiamei Deng
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Tracking Error ◽  
Reference Signal ◽  
Original System ◽  
Linear Matrix ◽  
Preview Control ◽  
Lipschitz Nonlinear Systems ◽  
Error System ◽  
Discrete Integrator

This paper considers the design of the robust preview controller for a class of uncertain discrete-time Lipschitz nonlinear systems. According to the preview control theory, an augmented error system including the tracking error and the known future information on the reference signal is constructed. To avoid static error, a discrete integrator is introduced. Using the linear matrix inequality (LMI) approach, a state feedback controller is developed to guarantee that the closed-loop system of the augmented error system is asymptotically stable with H∞ performance. Based on this, the robust preview tracking controller of the original system is obtained. Finally, two numerical examples are included to show the effectiveness of the proposed controller.

Sign in / Sign up

Export Citation Format

Share Document