Maximal perturbation bounds for the robust stability of fractional-order linear time-invariant parameter-dependent systems

2021 ◽  
pp. 1-1
Author(s):  
Ruo-Nan Qian ◽  
Jun-Guo Lu ◽  
Qing-Hao Zhang
Keyword(s):  
Fractional Order ◽  
Robust Stability ◽  
Linear Time ◽  
Order Linear ◽  
Perturbation Bounds ◽  
Linear Time Invariant ◽  
Invariant Parameter ◽  
Parameter Dependent ◽  
Time Invariant

Fractional-order linear time invariant swarm systems: asymptotic swarm stability and time response analysis

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Mojtaba Soorki ◽  
Mohammad Tavazoei
Keyword(s):  
Fractional Order ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Time Response ◽  
Response Analysis ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Time Response Analysis ◽  
Necessary And Sufficient ◽  
Time Invariant

AbstractThis paper deals with fractional-order linear time invariant swarm systems. Necessary and sufficient conditions for asymptotic swarm stability of these systems are presented. Also, based on a time response analysis the speed of convergence in an asymptotically swarm stable fractional-order linear time invariant swarm system is investigated and compared with that of its integer-order counterpart. Numerical simulation results are presented to show the effectiveness of the paper results.

Robust Controllability of Interval Fractional Order Linear Time Invariant Systems

2005 ◽  
Author(s):  
Yang Quan Chen ◽  
Hyo-Sung Ahn ◽  
Dingyu¨ Xue
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Linear Time ◽  
Interval Uncertainty ◽  
State Matrix ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Robust Controllability ◽  
Time Invariant

We consider uncertain fractional-order linear time invariant (FO-LTI) systems with interval coefficients. Our focus is on the robust controllability issue for interval FO-LTI systems in state-space form. We re-visited the controllability problem for the case when there is no interval uncertainty. It turns out that the stability check for FO-LTI systems amounts to checking the conventional integer order state space using the same state matrix A and the input coupling matrix B. Based on this fact, we further show that, for interval FO-LTI systems, the key is to check the linear dependency of a set of interval vectors. Illustrative examples are presented.

scholarly journals Robust stabilization withH∞performance for a class of linear parameter-dependent systems

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Hamid Reza Karimi
Keyword(s):  
Linear Time ◽  
Robust Stabilization ◽  
State Feedback Control ◽  
Disturbance Attenuation ◽  
Linear Time Invariant ◽  
Quadratic Lyapunov Functions ◽  
Nonlinear Uncertainties ◽  
Invariant Parameter ◽  
Parameter Dependent ◽  
Time Invariant

We focus on the issue of robust stabilization withH∞performance for a class of linear time-invariant parameter-dependent systems under norm-bounded nonlinear uncertainties. By combining the idea of polynomially parameter-dependent quadratic Lyapunov functions and linear matrix inequalities formulations, some parameter-independent conditions with high precision are given to guarantee robust asymptotic stability and robust disturbance attenuation of the linear time-invariant parameter-dependent system in the presence of norm-bounded nonlinear uncertainties. The parameter-dependent state-feedback control is designed based on the Hamilton-Jacobi-Isaac (HJI) method. The applicability of the proposed design method is illustrated in a simple example.

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