scholarly journals A New Sufficient Condition for Checking the Robust Stabilization of Uncertain Descriptor Fractional-Order Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Hongxing Wang ◽  
Aijing Liu
Keyword(s):  
Fractional Order ◽  
Robust Stabilization ◽  
Order System ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
State Matrix ◽  
Time Invariant

We consider the robust asymptotical stabilization of uncertain a class of descriptor fractional-order systems. In the state matrix, we require that the parameter uncertainties are time-invariant and norm-bounded. We derive a sufficient condition for the system with the fractional-order α satisfying 1≤α<2 in terms of linear matrix inequalities (LMIs). The condition of the proposed stability criterion for fractional-order system is easy to be verified. An illustrative example is given to show that our result is effective.

D-Stability Based LMI Criteria of Stability and Stabilization for Fractional Order Systems

2015 ◽  
Author(s):  
XueFeng Zhang ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Feasible Solution ◽  
Order System ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Integer Order ◽  
Stability And Stabilization ◽  
The Stability ◽  
Conditions Of Stability

This paper considers the stability and stabilization of fractional order systems (FOS) with the fractional order α: 0 < α < 1 case. The equivalence between stability of fractional order systems and D–stability of a matrix A in specific region is proven. The criteria of stability and stabilization of fractional order system are presented. The conditions are expressed in terms of linear matrix inequalities (LMIs) which can be easily calculated with standard feasible solution problem in MATLAB LMI toolbox. When α = 1, the results reduce to the conditions of stability and stabilization of integer order systems. Numerical examples are given to verify the effectiveness of the criteria. With the approach proposed in this paper, we can analyze and design fractional order systems in the same way as what we do to the integer order system state-space models.

scholarly journals LMI Criteria for Admissibility and Robust Stabilization of Singular Fractional-Order Systems Possessing Poly-Topic Uncertainties

2020 ◽  
Vol 4 (4) ◽  
pp. 58
Author(s):  
Xuefeng Zhang ◽  
Jia Dong
Keyword(s):  
Fractional Order ◽  
Linear Matrix Inequalities ◽  
State Feedback ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Polytopic Uncertainties ◽  
And Control ◽  
Uncertain Linear Systems

The issue of robust admissibility and control for singular fractional-order systems (FOSs) with polytopic uncertainties is investigated in this paper. Firstly, a new method based on linear matrix inequalities (LMIs) is presented to solve the admissibility problems of uncertain linear systems. Then, a solid criterion of robust admissibility and a corresponding state feedback controller are derived, which overcome the conservatism of the existing results. Finally, for the sake of demonstrating the validity of proposed results, some relevant examples are provided.

State Feedback Robust H∞ Control for Generalized Discrete System and Simulation

2013 ◽  
Vol 467 ◽  
pp. 621-626
Author(s):  
Chen Fang ◽  
Jiang Hong Shi ◽  
Kun Yu Li ◽  
Zheng Wang
Keyword(s):  
Discrete System ◽  
State Feedback ◽  
Closed Loop ◽  
The State ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Closed Loop Systems

For a class of uncertain generalized discrete linear system with norm-bounded parameter uncertainties, the state feedback robust control problem is studied. One sufficient condition for the solvability of the problem and the state feedback robust controller are obtained in terms of linear matrix inequalities. The designed controller guarantees that the closed-loop systems is regular, causal, stable and satisfies a prescribed norm bounded constraint for all admissible uncertain parameters under some conditions. The result of the normal discrete system can be regarded as a particular form of our conclusion. A simulation example is given to demonstrate the effectiveness of the proposed method.

scholarly journals Robust Stabilization of Stochastic Markovian Jump Systems with Distributed Delays

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Guilei Chen ◽  
Zhenwei Zhang ◽  
Chao Li ◽  
Dianju Qiao ◽  
Bo Sun
Keyword(s):  
Linear Matrix Inequalities ◽  
Robust Stabilization ◽  
Distributed Delays ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Parameter Uncertainties ◽  
Delay Dependent ◽  
Jump Systems

This paper addresses the robust stabilization problem for a class of stochastic Markovian jump systems with distributed delays. The systems under consideration involve Brownian motion, Markov chains, distributed delays, and parameter uncertainties. By an appropriate Lyapunov–Krasovskii functional, the novel delay-dependent stabilization criterion for the stochastic Markovian jump systems is derived in terms of linear matrix inequalities. When given linear matrix inequalities are feasible, an explicit expression of the desired state feedback controller is given. The designed controller, based on the obtained criterion, ensures asymptotically stable in the mean square sense of the resulting closed-loop system. The convenience of the design is greatly enhanced due to the existence of an adjustable parameter in the controller. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed theory.

scholarly journals Robust Stability and Stabilization of Interval Uncertain Descriptor Fractional-Order Systems with the Fractional-Orderα: The1≤α<2Case

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yuanhua Li ◽  
Heng Liu ◽  
Hongxing Wang
Keyword(s):  
Fractional Order ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Interval System ◽  
Interval Coefficients ◽  
Stability And Stabilization ◽  
Necessary And Sufficient ◽  
Robust Stability And Stabilization

Stability and stabilization of fractional-order interval system is investigated. By adding parameters to linear matrix inequalities, necessary and sufficient conditions for stability and stabilization of the system are obtained. The results on stability check for uncertain FO-LTI systems with interval coefficients of dimensionnonly need to solve one 4n-by-4nLMI. Numerical examples are presented to shown the effectiveness of our results.

Improvement of Admissibility of Linear Singular Fractional Order Systems

2019 ◽  
Author(s):  
XueFeng Zhang ◽  
Yingbo Zhang
Keyword(s):  
Fractional Order ◽  
Linear Matrix Inequalities ◽  
Equality Constraint ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Decision Variables ◽  
Strict Lmis ◽  
New Criteria

Abstract This paper considers the least solutions of linear matrix inequalities (LMIs) in criteria of admissibility for continuous singular fractional order systems (FOS). The new criteria are given which are strict LMIs and do not involve equality constraint and with the less LMI decision variables. With brief and simple results of this paper, the numbers of solved matrices are reduced from a pair of matrices to just a matrix in which we can analyze singular fractional order systems with completely consistent format as normal systems.

scholarly journals Robust and NonfragileH∞Kalman-Type Filter Design for Parameter-Uncertain Time-Delay Systems: PLMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Seung Hyeop Yang ◽  
Hong Bae Park
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Filter Design ◽  
Estimation Error ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Parameter Uncertainties

This paper describes the synthesis of a robust and nonfragileH∞Kalman-type filter design for a class of time-delay systems with polytopic uncertainties, filter-gain variations, and disturbances. We present the sufficient condition for filter existence and the method for designing a robust nonfragileH∞filter by using LMIs (Linear Matrix Inequalities) technique. Because the obtained sufficient condition can be represented as PLMIs (Parameterized Linear Matrix Inequalities), which can generate infinite LMIs, we use a relaxation technique to find finite solutions for a robust nonfragileH∞filter. We show that the proposed filter can minimize estimation error in terms of parameter uncertainties, filter-fragility, and disturbances.

New criteria for dissipativity analysis of Caputo fractional-order neural networks with non-differentiable time-varying delays

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Nguyen Thi Phuong ◽  
Nguyen Thi Thanh Huyen ◽  
Nguyen Thi Huyen Thu ◽  
Nguyen Huu Sau ◽  
Mai Viet Thuan
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Simulation Results ◽  
Delay Dependent ◽  
Dissipativity Analysis ◽  
New Criteria

Abstract In this article, we investigate the delay-dependent and order-dependent dissipativity analysis for a class of Caputo fractional-order neural networks (FONNs) subject to time-varying delays. By employing the Razumikhin fractional-order (RFO) approach combined with linear matrix inequalities (LMIs) techniques, a new sufficient condition is derived to guarantee that the considered fractional-order is strictly (Q, S, R) − γ − dissipativity. The condition is presented via LMIs and can be efficiently checked. Two numerical examples and simulation results are finally provided to express the effectiveness of the obtained results.

Robust and Non-Fragile H∞ Observer-Based Filter Design for Parameter Uncertain System Using PLMI Approach

2013 ◽  
Vol 373-375 ◽  
pp. 685-688
Author(s):  
Seung Hyeop Yang ◽  
Seung Hyun Paik ◽  
Hong Bae Park
Keyword(s):  
Linear Matrix Inequalities ◽  
Filter Design ◽  
Estimation Error ◽  
Uncertain System ◽  
Relaxation Technique ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Polytopic Uncertainties

This paper describes the synthesis of a robust and non-fragile H∞ observer-based filter design for a class of parameter uncertain system with polytopic uncertainties, disturbances, and gain variations. We present the sufficient condition for filter existence and the method for designing a robust and non-fragile H∞ filter by using LMIs (Linear Matrix Inequalities) technique. Because the obtained sufficient condition can be represented as PLMIs (Parameterized Linear Matrix Inequalities), which can generate infinite LMIs, we use the relaxation technique to find finite solutions for a robust and non-fragile H∞ filter. We show that the proposed filter can minimize the estimation error in terms of parameter uncertainties, filter-fragility, and disturbances.

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