Full-Order and Reduced-Order Exponential Observers for Discrete-Time Nonlinear Systems With Incremental Quadratic Constraints

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Wei Zhang ◽  
Younan Zhao ◽  
Masoud Abbaszadeh ◽  
Mingming Ji
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Exponential Convergence ◽  
Estimation Error ◽  
Observer Design ◽  
Linear Matrix ◽  
Discrete Time System ◽  
Quadratic Constraints ◽  
Reduced Order ◽  
Reduced Order Observer

This paper considers the observer design problem for a class of discrete-time system whose nonlinear time-varying terms satisfy incremental quadratic constraints. We first construct a circle criterion based full-order observer by injecting output estimation error into the observer nonlinear terms. We also construct a reduced-order observer to estimate the unmeasured system state. The proposed observers guarantee exponential convergence of the state estimation error to zero. The design of the proposed observers is reduced to solving a set of linear matrix inequalities. It is proved that the conditions under which a full-order observer exists also guarantee the existence of a reduced-order observer. Compared to some previous results in the literature, this work considers a larger class of nonlinearities and unifies some related observer designs for discrete-time nonlinear systems. Finally, a numerical example is included to illustrate the effectiveness of the proposed design.

Reduced-Order Observer Design for Discrete-Time Descriptor Systems With Unknown Inputs: An Linear Matrix Inequality Approach

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Shenghui Guo ◽  
Fanglai Zhu
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Observer Design ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Unknown Input ◽  
Matrix Inequality ◽  
Reduced Order ◽  
Unknown Inputs ◽  
Reduced Order Observer

Reduced-order observer design methods for both linear and nonlinear discrete-time descriptor systems based on the linear matrix inequality (LMI) approach are investigated. We conclude that the conditions under which a full-order observer exists can also guarantee the existence of a reduced-order observer. By choosing a special reduced-order observer gain matrix, a reduced-order unknown input observer is proposed for linear system with unknown inputs, and then an unknown input reconstruction is provided for some special cases. We also extend above results to the cases of nonlinear systems. Finally, three numerical comparative simulation examples are given to illustrate the effectiveness and merits of proposed methods.

scholarly journals Observer Design for Simultaneous State and Fault Estimation for a Class of Discrete-time Descriptor Linear Models

2021 ◽  
Vol 229 ◽  
pp. 01020
Author(s):  
Kaoutar Ouarid ◽  
Abdellatif El Assoudi ◽  
Jalal Soulami ◽  
El Hassane El Yaagoubi
Keyword(s):  
Discrete Time ◽  
Linear Models ◽  
Estimation Error ◽  
Equivalent Form ◽  
Observer Design ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Sensor Faults ◽  
Actuator Faults ◽  
Algebraic Equations

This paper investigates the problem of observer design for simultaneous states and faults estimation for a class of discrete-time descriptor linear models in presence of actuator and sensor faults. The idea of the present result is based on the second equivalent form of implicit model [1] which permits to separate the differential and algebraic equations in the considered singular model, and the use of an explicit augmented model structure. At that stage, an observer is built to estimate simultaneously the unknown states, the actuator faults, and the sensor faults. Next, the explicit structure of the augmented model is established. Then, an observer is built to estimate simultaneously the unknown states, the actuator faults, and the sensor faults. By using the Lyapunov approach, the convergence of the state estimation error of the augmented system is analyzed, and the observer’s gain matrix is achieved by solving only one linear matrix inequality (LMI). At long last, an illustrative model is given to show the performance and capability of the proposed strategy.

scholarly journals Invariant Manifold Based Reduced-Order Observer Design for Nonlinear Systems

2008 ◽  
Vol 53 (11) ◽  
pp. 2602-2614 ◽  
Author(s):  
Dimitrios Karagiannis ◽  
Daniele Carnevale ◽  
Alessandro Astolfi
Keyword(s):  
Nonlinear Systems ◽  
Invariant Manifold ◽  
Observer Design ◽  
Reduced Order ◽  
Reduced Order Observer

scholarly journals PI Observer Design for a Class of Nondifferentially Flat Systems

2019 ◽  
Vol 29 (4) ◽  
pp. 655-665
Author(s):  
Juan Pablo Flores-Flores ◽  
Rafael Martinez-Guerra
Keyword(s):  
Design Methodology ◽  
Estimation Error ◽  
Differential Algebra ◽  
Point Of View ◽  
Observer Design ◽  
Differential Polynomials ◽  
Reduced Order ◽  
Model Free ◽  
Flat Systems ◽  
Reduced Order Observer

Abstract This paper presents a methodology and design of a model-free-based proportional-integral reduced-order observer for a class of nondifferentially flat systems. The problem is tackled from a differential algebra point of view, that is, the state observer for nondifferentially flat systems is based on algebraic differential polynomials of the output. The observation problem is treated together with that of a synchronization between a chaotic system and the designed observer. Some basic notions of differential algebra and concepts related to chaotic synchronization are introduced. The PI observer design methodology is given and it is proven that the estimation error is uniformly ultimately bounded. To exemplify the effectiveness of the PI observer, some cases and their respective numerical simulation results are presented.

Full-Order and Reduced-order Observer Design for a Class of Fractional-order Nonlinear Systems

2016 ◽  
Vol 18 (4) ◽  
pp. 1467-1477 ◽  
Author(s):  
Yong-Hong Lan ◽  
Liang-Liang Wang ◽  
Lei Ding ◽  
Yong Zhou
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
Observer Design ◽  
Reduced Order ◽  
Reduced Order Observer

Stochastically Resilient Observer Design for a Class of Discrete-Time Nonlinear Systems

2011 ◽  
Author(s):  
Chung Seop Jeong ◽  
Edwin E. Yaz ◽  
Yvonne I. Yaz
Keyword(s):  
Discrete Time ◽  
Estimation Error ◽  
Finite Energy ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Performance Criteria ◽  
Linear Matrix ◽  
Computational Errors ◽  
Simple Estimation ◽  
Measurement Equations

A class of discrete-time nonlinear system and measurement equations having incrementally conic nonlinearities and finite energy disturbances is considered. A linear matrix inequality based nonlinear observer design approach is presented, which guarantees the satisfaction of a variety of performance criteria ranging from simple estimation error boundedness to dissipativity in the presence of random perturbations, due possibly to computational errors or changes during operation, on the observer gain. Some simulation examples are included to illustrate the proposed design methodology.

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