The Use of Partial Stability in the Analysis of Interconnected Systems

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Bo Wang ◽  
Hashem Ashrafiuon ◽  
Sergey G. Nersesov
Keyword(s):  
Sufficient Conditions ◽  
Control Design ◽  
Interconnected Systems ◽  
System State ◽  
Uniform Asymptotic Stability ◽  
Partial Stability ◽  
Control Framework ◽  
Control Objective ◽  
The Stability ◽  
Robot Platform

Abstract In this paper, we develop sufficient conditions for uniform asymptotic stability of interconnected dynamical systems that are not in cascade form. We show that the stability analysis of a two-subsystem interconnection can be reduced to ensuring the stability of the first nonisolated subsystem with respect to its own state vector (partial stability) and the stability of the isolated second subsystem. In addition, based on the above results, we provide a control design framework for nonlinear systems where the control objective reduces to stabilization of only a part of the system state while guaranteeing the stability for the entire state of the system. We validate the efficacy of the proposed control framework via simulations and experiments using the wheeled mobile robot platform.

scholarly journals Stability of Infinite Dimensional Interconnected Systems with Impulsive and Stochastic Disturbances

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Xiaohui Xu ◽  
Xiaofeng Yin ◽  
Jiye Zhang ◽  
Peng Wang
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Interconnected Systems ◽  
Stochastic Disturbances ◽  
Infinite Dimensional ◽  
Disturbance Propagation ◽  
Vector Lyapunov Function ◽  
Look Ahead ◽  
The Stability

Some research on the stability with mode constraint for a class of infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances is studied by using the vector Lyapunov function approach. Intuitively, the stability with mode constraint is the property of damping disturbance propagation. Firstly, we derive a set of sufficient conditions to assure the stability with mode constraint for a class of general infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances. The obtained conditions are less conservative than the existing ones. Secondly, the controller for a class of look-ahead vehicle following systems with the above uncertainties is constructed by the sliding mode control method. Based on the obtained new stability conditions, the domain of the control parameters of the systems is proposed. Finally, a numerical example with simulations is given to show the effectiveness and correctness of the obtained results.

scholarly journals New Decentralized Control of Interconnected Systems

2020 ◽  
Vol 9 (4) ◽  
pp. 2252-2260
Keyword(s):  
Closed Loop ◽  
Sufficient Conditions ◽  
Interconnected Systems ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Matrix Inequalities ◽  
Interconnected System ◽  
Local Controller ◽  
The Stability ◽  
Finsler’S Lemma

In this paper, we present a new decentralized H∞ control for interconnected systems, the interconnected system consists of several subsystems. The proposed approach based on Lyapunov functional and a H∞ criterion, employed to reduce the effect of interconnections between subsystems. In the first, we study the stability of the global system in closed loop using a criterion H∞, the stability conditions are presented in terms of LMI. In the second, to improve this approach, a Finsler’s lemma is used for the stability analysis by LMIs. Some sufficient conditions, ensuring all the closed-loop stability are supplied in terms of Linear Matrix Inequalities (LMIs), and the new feedback gain matrix of each local controller is obtained by solving the LMIs. Finally, the practice examples are given to illustrate the efficiency of the present method

scholarly journals On uniform asymptotic stability for nonlinear integro-differential equations of Volterra type

2019 ◽  
pp. 161-166
Author(s):  
Natalia Sedova
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Auxiliary Function ◽  
Uniform Asymptotic Stability ◽  
Volterra Type ◽  
Razumikhin Technique ◽  
The Stability ◽  
The Right

The specifics of the application of Razumikhin technique to the stability analysis of Volterra type integrodifferential equations are considered. The equation can be nonlinear and nonautonomous. We propose new sufficient conditions for uniform asymptotic stability of the zero solution using the phase space of a special construction and constraints on the right side of the equation. In the presented constraints we can analyze stability, relying not only on the behavior of the auxiliary function along the solutions, but also on the properties of the so called limiting equations.

scholarly journals On Stability of Linear Delay Differential Equations under Perron's Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
J. Diblík ◽  
A. Zafer
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Uniform Asymptotic Stability ◽  
Linear Delay ◽  
Functional Differential ◽  
The Stability ◽  
Delay Differential

The stability of the zero solution of a system of first-order linear functional differential equations with nonconstant delay is considered. Sufficient conditions for stability, uniform stability, asymptotic stability, and uniform asymptotic stability are established.

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 Integro-differential equations of Volterra type

1970 ◽  
Vol 3 (1) ◽  
pp. 9-22 ◽  
Author(s):  
M. Rama Mohana Rao ◽  
Chris P. Tsokos
Keyword(s):  
Differential System ◽  
Basic Result ◽  
Sufficient Conditions ◽  
Continuous Operator ◽  
Continuous Functions ◽  
Uniform Asymptotic Stability ◽  
Space Of Continuous Functions ◽  
Volterra Type ◽  
The Stability ◽  
Image Position

The aim of this paper is concerned with studying the stability properties of an integro-differential system by reducing it into a scalar integro-differential equation. A theorem is stated about the existence of a maximal solution of such systems and a basic result on integro-differential inequalities. Utilizing these results we obtain sufficient conditions for uniform asymptotic stability of the trivial solution of the integro-differential system of the form where , with , , C(J) denotes the space of continuous functions, A a continuous operator such that A maps C(J) into C(J). The fruitfulness of the results of the paper are illustrated with two applications.

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

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