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.

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 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.

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.

The Application of Linear Algebra Algorithm in the Production of Linear Matrix Inequalities

2012 ◽  
Vol 192 ◽  
pp. 406-411
Author(s):  
Hui Zhang
Keyword(s):  
Problem Solving ◽  
Linear Algebra ◽  
Linear Matrix Inequalities ◽  
Polynomial Matrix ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Application System ◽  
And Control ◽  
Problem Data

Discusses the theory and symbolic of the algorithm gives another potential application, but also in the system and control. For example, for the question, has made with special structure, but LMI problem data, may cause factorizations LMI more compact. One can even imagine using the algorithm around, looking for the opportunity to LMI automatic eliminate variables, so simplify problem solving, before they get a lot of influence and a potential solutions. We describe theory, the algorithm can be used to factor in the non commuting variable polynomial matrix and application system switches and control problem into a linear matrix inequality.

Mixed H2/H∞ Control for State-Delayed Linear Systems and a LMI Approach to the Solution of Coupled AREs

2003 ◽  
Vol 125 (2) ◽  
pp. 249-253 ◽  
Author(s):  
M. D. S. Aliyu
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Linear Matrix Inequalities ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Riccati Equations ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lmi Approach ◽  
Alternative Approach

In this paper, the state-feedback mixed H2/H∞ control problem for state-delayed linear systems is considered. Sufficient conditions for the solvability of this problem are given in terms of the solution to a pair of algebraic Riccati equations similar to the nondelayed case. However, these Riccati equations are more difficult to solve than those arising in the pure H2,H∞ problems, and an alternative approach is to solve a pair of linear matrix inequalities (LMIs).

Linear Matrix Inequalities in System and Control Theory

1994 ◽  
Author(s):  
Stephen Boyd ◽  
Laurent El Ghaoui ◽  
Eric Feron ◽  
Venkataramanan Balakrishnan
Keyword(s):  
Control Theory ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
And Control

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.

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