The Unknown Input Reconstruction and Reduced-Order Observer Design of Discrete Time T-S Fuzzy System

2016 ◽  
Author(s):  
Ming Cai ◽  
Fengning Wang
Keyword(s):  
Discrete Time ◽  
Fuzzy System ◽  
Observer Design ◽  
Unknown Input ◽  
Reduced Order ◽  
Reduced Order Observer ◽  
Input Reconstruction

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.

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 with unknown input for fractional order descriptor nonlinear systems

2019 ◽  
Vol 41 (13) ◽  
pp. 3705-3713 ◽  
Author(s):  
Tao Zhan ◽  
Shuping Ma
Keyword(s):  
Fractional Order ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Order Reduction ◽  
Electrical Circuit ◽  
Observer Design ◽  
Unknown Input ◽  
Reduced Order ◽  
The Matrix ◽  
Reduced Order Observer

This paper investigates the observer design issues for the quadratic inner-bounded nonlinear descriptor fractional order systems. Considering the disturbances or inaccessible partial inputs, the order reduction of observer with unknown input is firstly implemented for effectively estimating the system state vectors. Then, for the purpose of the system conservatism reduction, the matrix [Formula: see text] and the matrix generalized inverse technique are applied to design the reduced-order observer, which can deal with unknown input with less restrictions of coefficient matrices. By using fractional order Lyapunov direct method, sufficient conditions can be obtained to ensure the existence of the designed observer. Finally, a fractional order electrical circuit is applied to demonstrate the applicability of the proposed approach.

scholarly journals Decentralized Polynomial Observer Design for Discrete-Time Large-Scale Polynomial T-S Fuzzy System

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Seung-Hun Han ◽  
Van-Phong Vu ◽  
Manh-Son Tran
Keyword(s):  
Nonlinear System ◽  
Discrete Time ◽  
Fuzzy System ◽  
Large Scale ◽  
Observer Design ◽  
Unknown Input ◽  
New Approach ◽  
Unknown Inputs ◽  
Input Method ◽  
Takagi Sugeno

In this paper, a new approach for synthesizing a decentralized observer is proposed to estimate the unmeasurable states of a discrete-time large-scale nonlinear system. The large-scale nonlinear system in this study is modeled in terms of a set of discrete-time polynomial Takagi-Sugeno (T-S) fuzzy subsystems and interconnection terms. This modeling method will assist to reduce significantly the number of fuzzy rules. The interconnection terms are considered as the unknown inputs; then, the unknown input method is employed to design observer for this system. It should be emphasized that the interconnection parts in this paper are arbitrary and their effects are eliminated completely. On the basis of the Lyapunov methodology and SOS (Sum of Square) technique, the conditions for observer design expressed under the framework of SOS are derived in the main theorems. Finally, an illustrative example is presented to show the effectiveness and merit of the proposed method.

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