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.

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.

Unfragile Passive Control of Uncertain Sampling System

2013 ◽  
Vol 325-326 ◽  
pp. 1170-1175
Author(s):  
Qing Zhi Liu
Keyword(s):  
Control Problem ◽  
Robust Stability ◽  
Passive Control ◽  
Lyapunov Method ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Sampling System ◽  
State Delay ◽  
Index Terms

The unfragile passive control problem of a class of uncertain state-delay sampling system is discussed. Applying Lyapunov method, and combining the properties of matrix inequality, the sufficient condition of robust stability is given, and the unfragile passive controller is designed. Finally a numerical example illustrates the effectiveness and the availability for the design.Index Terms - Uncertain State-delay Sampling System , Linear Matrix Inequility , Unfragile Passive Control .

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 passivity results for the realization of interfered digital filters utilizing saturation overflow nonlinearities

2018 ◽  
Vol 40 (15) ◽  
pp. 4246-4252 ◽  
Author(s):  
CG Parthipan ◽  
Xavier S Arockiaraj ◽  
Priyanka Kokil
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
State Space ◽  
Digital Filters ◽  
Linear Matrix ◽  
Input State ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
External Interference ◽  
Simulation Results

This paper considers the passivity performance analysis of fixed-point state-space digital filters with saturation nonlinearities in the presence of external interference. The purpose is to establish new stability criteria in terms of linear matrix inequality (LMI) such that fixed-point state-space digital filters with saturation nonlinearities in the existence of external interference ensure passivity performance with its storage function. The presented results not only ensure state strict and input state strict passivity in the presence of external interference but also confirm asymptotic stability without external interference. The obtained conditions for fixed-point state-space digital filters are based on passivity properties and, hence, are quite novel to previously proposed criteria. Finally, simulation results are given to demonstrate the effectiveness of the proposed work.

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.

Novel ISS criteria for digital filters using generalized overflow non-linearities and external interference

2018 ◽  
Vol 41 (1) ◽  
pp. 156-164 ◽  
Author(s):  
Mani Kant Kumar ◽  
Priyanka Kokil ◽  
Haranath Kar
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Linear Matrix Inequality ◽  
State Space ◽  
Digital Filters ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
External Interference ◽  
Simulation Results

Sufficient criteria for input-to-state stability (ISS) of fixed-point state-space interfered digital filters with generalized overflow non-linearities are presented. The generalized overflow non-linearities under consideration cover the usual types of overflow arithmetic employed in practice, such as saturation, zeroing, two’s complement and triangular. The criteria not only ensure diminishing consequence of external interference but also confirm the asymptotic stability of the system when external interference disappears. The criteria are derived in the linear matrix inequality (LMI) framework. Simulation results are provided to illustrate the utility of the presented approach. With the help of one example, it is illustrated that the presented approach can lead to a less stringent ISS condition for the digital filters with saturation non-linearities compared with a previously reported approach.

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.

Robust Nonfragile Decentralized Controller Design for Uncertain Large-Scale Interconnected Systems With Time-Delays

2002 ◽  
Vol 124 (2) ◽  
pp. 332-336 ◽  
Author(s):  
Ju H. Park
Keyword(s):  
Time Delays ◽  
Large Scale ◽  
Lyapunov Method ◽  
Controller Design ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Large Scale Systems ◽  
Controller Gain ◽  
Decentralized Controllers

This paper describes the synthesis of robust nonfragile decentralized controllers for uncertain large-scale systems with time-delays in the subsystem interconnections and controller gain variations. Based on the Lyapunov method, a sufficient condition for robust stability is derived in terms of a linear matrix inequality (LMI), and the measure of nonfragility in controller is presented.

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