The stability analysis of nonlinear switched systems with time delay in input and states with stable and unstable subsystems

2018 ◽  
Vol 40 (16) ◽  
pp. 4298-4308 ◽  
Author(s):  
Zeinab Echreshavi ◽  
Alireza Roosta
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Sufficient Conditions ◽  
Switched System ◽  
Control Laws ◽  
Nonlinear Switched Systems ◽  
Unstable Subsystems ◽  
Measurement Delay ◽  
The Stability ◽  
System With Time Delay

Time delay and sampling appear in many industrial systems. It is irrefutable that applying measurement delay with controls can cause the sampling of control laws with the delay in the behavior of nonlinear control systems. As a result, in this paper, the stability of nonlinear time varying switched system with time delay in the input and the states of the system is studied in two modes by a new Lyapunov Krasovskii functional (LKF). Firstly, if all subsystems of the proposed nonlinear switched system with time delay are stable. Then, if some of the subsystems of the proposed switched system are unstable. This paper is organized in two steps. In the first step, the upper bound for the time delay under sufficient conditions in the nonlinear systems with time delay in input and states is obtained. In this step, the Uniformly Globally Asymptotic Stability is proved for nonlinear systems with the presence of time delay. In the second step, with a proper Lyapunov Krasovskii functional, the global exponential stability of the proposed switched system is proved. Also, finally a proper observer is designed for our proposed switched system in two stable and unstable modes.

Stability analysis and stabilization of a class of discrete-time nonlinear switched systems with time-delay and affine parametric uncertainty

2019 ◽  
Vol 25 (7) ◽  
pp. 1326-1340 ◽  
Author(s):  
N.A. Baleghi ◽  
M.H. Shafiei
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Sufficient Conditions ◽  
Parametric Uncertainty ◽  
Switched System ◽  
Time Varying Delay ◽  
Nonlinear Switched Systems ◽  
The Stability ◽  
Varying Delay ◽  
Special Case

This paper presents stability analysis and stabilization of a nonlinear switched system with subsystems which involve time-varying delay, nonlinear terms, and affine parametric uncertainties. The main goal of this paper is to construct a state-feedback controller to stabilize the closed-loop switched system, and as a special case to derive sufficient conditions to guarantee the stability of the uncontrolled switched system. In this regard, based on switched Lyapunov functions, an appropriate Lyapunov–Krasovskii functional is constructed to establish the sufficient conditions; these conditions depend only on the upper bounds of the time-delay, uncertain parameters, and the maximal bound of the nonlinear term. Finally, numerical examples are provided to verify the theoretical results and to compare the obtained results with previous researches.

scholarly journals Finite-time stability of multiterm fractional nonlinear systems with multistate time delay

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
G. Arthi ◽  
N. Brindha ◽  
Yong-Ki Ma
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
The Novel ◽  
Finite Range ◽  
Time Stability ◽  
Finite Time Stability ◽  
Fractional System ◽  
The Stability

AbstractThis work is mainly concentrated on finite-time stability of multiterm fractional system for $0 < \alpha _{2} \leq 1 < \alpha _{1} \leq 2$ 0 < α 2 ≤ 1 < α 1 ≤ 2 with multistate time delay. Considering the Caputo derivative and generalized Gronwall inequality, we formulate the novel sufficient conditions such that the multiterm nonlinear fractional system is finite time stable. Further, we extend the result of stability in the finite range of time to the multiterm fractional integro-differential system with multistate time delay for the same order by obtaining some inequality using the Gronwall approach. Finally, from the examples, the advantage of presented scheme can guarantee the stability in the finite range of time of considered systems.

Uniform Stability of Discrete-Time Switched Nonlinear Systems

2014 ◽  
Vol 643 ◽  
pp. 83-89
Author(s):  
Shu Rong Sun ◽  
Guang Rong Zhang ◽  
Ping Zhao
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Uniform Stability ◽  
Switched Nonlinear Systems ◽  
Uniform Asymptotic Stability ◽  
Unstable Subsystems ◽  
The Stability

In this paper, we study the stability properties of a general class of nonautonomous discrete-time switched nonlinear systems. The switched systems consist of stable and unstable subsystems. Based on Lyapunov functions, some sufficient conditions for uniform stability, uniform asymptotic stability and uniform exponential stability are established.

scholarly journals Almost Global Stability of Nonlinear Switched System with Stable and Unstable Subsystems

2020 ◽  
Author(s):  
Aysegul Kivilcim ◽  
Ozkan Karabacak ◽  
Rafal Wisniewski
Keyword(s):  
Global Stability ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Operation Time ◽  
Average Dwell Time ◽  
Fast Switching ◽  
Nonlinear Switched Systems ◽  
Unstable Subsystems ◽  
The Stability ◽  
Slow Switching

This paper presents sufficient conditions for almost global stability of nonlinear switched systems consisting of both stable and unstable subsystems. Techniques from the stability analysis of switched systems have been combined with the multiple Lyapunov density approach - recently proposed by the authors for the almost global stability of nonlinear switched systems composed of stable subsystems. By using slow switching for stable subsystems and fast switching for unstable subsystems lower and upper bounds for mode-dependent average dwell times are obtained. In addition to that, by allowing each subsystem to perform slow switching and using some restrictions on total operation time of unstable subsystems and stable subsystems, we have obtained a lower bound for an average dwell time.

Adaptive event-triggered control for master-slave switched systems subject to attacked state-dependent switching law

2021 ◽  
pp. 014233122098594
Author(s):  
Lingcong Nie ◽  
Xindi Xu ◽  
Yan Li ◽  
Weiyu Jiang ◽  
Yiwen Qi ◽  
...  
Keyword(s):  
Time Delay ◽  
Switched Systems ◽  
System Performance ◽  
Actuator Saturation ◽  
Sufficient Conditions ◽  
Switched System ◽  
Switching Law ◽  
Variable Threshold ◽  
Event Triggering ◽  
Event Triggered

This paper investigates adaptive event-triggered [Formula: see text] control for network-based master-slave switched systems subject to actuator saturation and data injection attacks. It is an important and unrecognised issue that the switching signal is affected from both event-triggering scheme and network attacks. An adaptive event-triggering scheme is proposed that can adjust the triggering frequency through a variable threshold based on system performance. Furthermore, considering the impacts of transmission delays and actuator saturation, an event-triggered time-delay error switched system is developed. Subsequently, by utilizing piecewise Lyapunov functional technique, sufficient conditions are derived to render the time-delay error switched system to have an [Formula: see text] performance level. In particular, the coupling between switching instants and data updating instants is analyzed during the system performance analysis. Moreover, sufficient conditions for the desired state-feedback controller gains and event-triggering parameter are presented. Finally, a numerical example is given to verify the effectiveness of the proposed method.

scholarly journals Global Exponential Robust Stability of Static Interval Neural Networks with Time Delay in the Leakage Term

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guiying Chen ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Leakage Term ◽  
Interval Neural Networks ◽  
Global Exponential Robust Stability ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

The stability of a class of static interval neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, we obtain some sufficient conditions ensuring the global exponential robust stability of the networks. The results in this paper extend the corresponding conclusions without leakage delay. An example is given to illustrate the effectiveness of the obtained results.

Stabilizing Feedback Controls for Nonlinear Hamiltonian Systems and Nonconservative Bilinear Systems in Elasticity

1982 ◽  
Vol 104 (1) ◽  
pp. 27-32 ◽  
Author(s):  
S. N. Singh
Keyword(s):  
Asymptotic Stability ◽  
Hamiltonian Systems ◽  
Attitude Control ◽  
Sufficient Conditions ◽  
Bilinear Systems ◽  
Feedback Controls ◽  
Control Laws ◽  
Nonlinear Maps ◽  
The Stability ◽  
Necessary And Sufficient

Using the invariance principle of LaSalle [1], sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.

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 Mathematical analysis of a cancer model with time-delay in tumor-immune interaction and stimulation processes

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kaushik Dehingia ◽  
Hemanta Kumar Sarmah ◽  
Yamen Alharbi ◽  
Kamyar Hosseini
Keyword(s):  
Time Delay ◽  
Immune Responses ◽  
Periodic Solutions ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Cancer Model ◽  
Delay Effect ◽  
Discrete Time Delay ◽  
The Stability ◽  
Vital Parameters

AbstractIn this study, we discuss a cancer model considering discrete time-delay in tumor-immune interaction and stimulation processes. This study aims to analyze and observe the dynamics of the model along with variation of vital parameters and the delay effect on anti-tumor immune responses. We obtain sufficient conditions for the existence of equilibrium points and their stability. Existence of Hopf bifurcation at co-axial equilibrium is investigated. The stability of bifurcating periodic solutions is discussed, and the time length for which the solutions preserve the stability is estimated. Furthermore, we have derived the conditions for the direction of bifurcating periodic solutions. Theoretically, it was observed that the system undergoes different states if we vary the system’s parameters. Some numerical simulations are presented to verify the obtained mathematical results.

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