The Stability of a Class of Fractional Order Switching System with Time-Delay Actuator

2018 ◽  
Vol 7 (1) ◽  
pp. 85-96 ◽  
Author(s):  
Seyed Hossein Nabavi ◽  
Saeed Balochian
Keyword(s):  
Time Delay ◽  
Lyapunov Function ◽  
Fractional Order ◽  
Variable Structure ◽  
Linear Matrix ◽  
Switching Systems ◽  
Switching System ◽  
State Matrix ◽  
Switching Rule ◽  
The Impact

Since switching systems are important in research and industry, the article is concerned about the stabilization of fractional order switching systems with the order of 1 < q < 2 and a time delay actuator. To this end, the so-called system was initially converted to a system with no delay using a trick, such that the impact of delay was considered in the state matrix of the system in form of a coefficient. In the following, the switching rule was obtained based on the variable structure control with the sliding section. The necessary stability condition for the fractional order switching system with the order of 1 < q < 2 and time delay actuator is presented and approved based on the convex analysis and linear matrix inequalities. Then, a Lyapunov function was introduced with its negative derivative. By defining the Lyapunov function, the system that can be chosen at any time by the switching rule would be stable. Finally, the simulation results were expressed to show the impact of the proposed method.

scholarly journals Robust Switching Rule Design for Boost Converters with Uncertain Parameters and Disturbances

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yang Yang ◽  
Hamid Reza Karimi ◽  
Zhengrong Xiang
Keyword(s):  
Lyapunov Function ◽  
Linear System ◽  
Design Problem ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Common Lyapunov Function ◽  
Reference Tracking ◽  
Boost Converters ◽  
Switching Rule

This paper is concerned with the design problem of robust switching rule for Boost converters with uncertain parameters and disturbances. Firstly, the Boost converter is modeled as a switched affine linear system with uncertain parameters and disturbances. Then, using common Lyapunov function approach and linear matrix inequality (LMI) technique, a novel switching rule is proposed such that the model reference tracking performance is satisfied. Finally, a simulation result is provided to show the validity of the proposed method.

Unknown input fractional-order functional observer design for one-side Lipschitz time-delay fractional-order systems

2019 ◽  
Vol 41 (15) ◽  
pp. 4311-4321 ◽  
Author(s):  
Mai Viet Thuan ◽  
Dinh Cong Huong ◽  
Nguyen Huu Sau ◽  
Quan Thai Ha
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Quadratic Function ◽  
Observer Design ◽  
Linear Matrix ◽  
Unknown Input ◽  
Functional Observer ◽  
The One

This paper addresses the problem of unknown input fractional-order functional state observer design for a class of fractional-order time-delay nonlinear systems. The nonlinearities consist of two parts where one part is assumed to satisfy both the one-sided Lipschitz condition and the quadratically inner-bounded condition and the other is not necessary to be Lipschitz and can be regarded as an unknown input, making the wider class of considered nonlinear systems. By taking the advantages of recent results on Caputo fractional derivative of a quadratic function, we derive new sufficient conditions with the form of linear matrix inequalities (LMIs) to guarantee the asymptotic stability of the systems. Four examples are also provided to show the effectiveness and applicability of the proposed method.

scholarly journals New observer-based control design for mismatched uncertain systems with time-delay

2016 ◽  
Vol 26 (4) ◽  
pp. 597-610 ◽  
Author(s):  
Van Van Huynh
Keyword(s):  
Time Delay ◽  
Estimation Error ◽  
The State ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
State Matrix ◽  
Control Techniques ◽  
Uncertain Time

Abstract In this paper, the state estimation problem for a class of mismatched uncertain time-delay systems is addressed. The estimation uses observer-based control techniques. The mismatched uncertain time-delay systems investigated in this study include mismatched parameter uncertainties in the state matrix and in the delayed state matrix. First, based on a new lemma with appropriately choosing Lyapunov functional, new results for stabilization of mismatched uncertain time-delay systems are provided on the basis of a linear matrix inequality (LMI) framework and the asymptotic convergence properties for the estimation error is ensured. Second, the control and observer gains are given from single LMI feasible solution which can overcome the drawback of the bilinear matrix inequalities approach often reported in the literature. Finally, a numerical example is used to demonstrate the efficacy of the proposed method.

scholarly journals Consensus Conditions for a Class of Fractional-Order Nonlinear Multiagent Systems with Constant and Time-Varying Time Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Xiaorong Zhang ◽  
Min Shi
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Fractional Order ◽  
Time Delays ◽  
Constant Time Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Varying Delay ◽  
Theoretical Results

The consensus problem for a class of fractional-order nonlinear multiagent systems with a distributed protocol containing input time delay is investigated in this paper. Consider both cases of constant time delay and time-varying delay, the delay-independent consensus conditions are obtained to achieve the consensus of the systems, respectively, by adopting the linear matrix inequality (LMI) methods and stability theory of fractional-order systems. As illustrated by the numerical examples, the proposed theoretical results work well and accurately.

scholarly journals A fractional-order love dynamical model with time delay for synergic couple : Stability analysis and Hopf bifurcation

2021 ◽  
Author(s):  
SANTOSHI PANIGRAHI ◽  
Sunita Chand ◽  
S Balamuralitharan
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Order Model ◽  
Fractional Order Model ◽  
The Stability ◽  
The Impact

We investigate the fractional order love dynamic model with time delay for synergic couples in this manuscript. The quantitative analysis of the model has been done where the asymptotic stability of the equilibrium points of the model have been analyzed. Under the impact of time delay, the Hopf bifurcation analysis of the model has been done. The stability analysis of the model has been studied with the reproduction number less than or greater than 1. By using Laplace transformation, the analysis of the model has been done. The analysis shows that the fractional order model with a time delay can sufficiently improve the components and invigorate the outcomes for either stable or unstable criteria. In this model, all unstable cases are converted to stable cases under neighbourhood points. For all parameters, the reproduction ranges have been described. Finally, to illustrate our derived results numerical simulations have been carried out by using MATLAB. Under the theoretical outcomes from parameter estimation, the love dynamical system is verified.

Robust adaptive control for a class of nonlinear switched systems using state-dependent switching

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Naeimadeen Noghredani ◽  
Naser Pariz
Keyword(s):  
Adaptive Control ◽  
Switched Systems ◽  
Variable Structure ◽  
Robust Adaptive Control ◽  
Linear Matrix ◽  
Switching Rule ◽  
Nonlinear Switched Systems ◽  
State Dependent ◽  
Robust Adaptive ◽  
The Stability

AbstractThis paper presents a novel adaptive control for a class of nonlinear switched systems by introducing a sufficient condition for stabilization. Based on the possible instability of all sub-systems, a variable structure (VS) switching rule with an adaptive approach and sliding sector was offered. Moreover, the stability condition of the system can be determined by solving linear matrix inequalities (LMIs) to ensure asymptotic stability. The application of H∞ analysis of nonlinear switched systems was also investigated through the design of the mentioned adaptive control system and defining a VS switching rule. Finally, simulation results were presented to validate the novelty of the proposed method.

Mittag–Leffler stability and finite-time control for a fractional-order hydraulic turbine governing system with mechanical time delay: An linear matrix inequalitie approach

2021 ◽  
pp. 107754632199759
Author(s):  
Peng Chen ◽  
Bin Wang ◽  
Yuqiang Tian ◽  
Ying Yang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Finite Time ◽  
Control Method ◽  
Hydraulic Turbine ◽  
System Stability ◽  
Linear Matrix ◽  
Time Control ◽  
Governing System ◽  
The Stability

This article mainly studies the Mittag–Leffler stability and finite-time control of a time-delay fractional-order hydraulic turbine governing system. First, properties of the Riemann–Liouville derivative and some important lemmas are introduced. Second, considering the mechanical time delay of the main servomotor, the mathematical model of a fractional-order hydraulic turbine governing system with mechanical time delay is presented. Then, based on Mittag–Leffler stability theorem, a suitable sliding surface and finite-time controller are designed for the hydraulic turbine governing system. The system stability is confirmed, and the stability condition is given in the form of linear matrix inequalities. Finally, the traditional proportional–integral–derivative control method and an existing sliding mode control method are selected to verify the effectiveness and robustness of the proposed method. This study also provides a new approach for the stability analysis of the time-delay fractional-order hydraulic turbine governing system.

scholarly journals Disturbance Rejection for Fractional-Order Time-Delay Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Hai-Peng Jiang ◽  
Yong-Qiang Liu
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Disturbance Rejection ◽  
Controller Design ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Design Algorithm ◽  
The Stability ◽  
Disturbance Estimator

This paper presents an equivalent-input-disturbance (EID-) based disturbance rejection method for fractional-order time-delay systems. First, a modified state observer is applied to reconstruct the state of the fractional-order time-delay plant. Then, a disturbance estimator is designed to actively compensate for the disturbances. Under such a construction of the system, by constructing a novel monochromatic Lyapunov function and using direct Lyapunov approach, the stability analysis and controller design algorithm are derived in terms of linear matrix inequality (LMI) technique. Finally, simulation results demonstrate the validity of the proposed method.

scholarly journals Stabilization of autonomous linear time invariant fractional order derivative switched systems with different derivative in subsystems

2014 ◽  
Vol 62 (3) ◽  
pp. 495-503 ◽  
Author(s):  
S. Balochian
Keyword(s):  
Fractional Order ◽  
Linear Time ◽  
Variable Structure ◽  
Switched System ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Linear Time Invariant ◽  
Necessary And Sufficient ◽  
Time Invariant ◽  
Derivative Order

Abstract In this paper, the stabilization problem of a autonomous linear time invariant fractional order (LTI-FO) switched system with different derivative order in subsystems is outlined. First, necessary and sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems based on the convex analysis and linear matrix inequality (LMI) for two subsystems is presented and proved. Also, sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems for more than two subsystems is proved. Then a sliding sector is designed for each subsystem of the LTI-FO switched system. Finally, a switching control law is designed to switch the LTI-FO switched system among subsystems to ensure the decrease of the norm of the switched system. Simulation results are given to show the effectiveness of the proposed variable structure controller.

scholarly journals Stability of Stochastic Differential Switching Systems with Time-Delay and Impulsive Effects

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Zhuang Fang ◽  
Xiaozhong Huang ◽  
Xuegang Tan
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Lyapunov Function ◽  
Global Exponential Stability ◽  
Stochastic Neural Networks ◽  
Switching Systems ◽  
Stability Criteria ◽  
Halanay’S Inequality ◽  
New Type ◽  
The Stability

This paper studies the stability of hybrid impulsive and switching stochastic neural networks. First, a new type of switching signal is constructed. The stochastic differential switching systems are steerable under the work of the switching signals. Then, using switching Lyapunov function approach, Itô formula, and generalized Halanay’s inequality, some global asymptotical and global exponential stability criteria are derived. These criteria improve the existing results on hybrid systems without noises. An example is given to demonstrate the effectiveness of the results.

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