An improved result for the stability of interconnected systems based on a new Gersgorin-type criterion

2007 ◽  
Author(s):  
Dimos V. Dimarogonas ◽  
Kostas J. Kyriakopoulos
Keyword(s):  
Interconnected Systems ◽  
Type Criterion ◽  
The Stability

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.

STABILITY ANALYSIS OF NONLINEAR INTERCONNECTED SYSTEMS VIA T–S FUZZY MODELS

2004 ◽  
Vol 04 (01) ◽  
pp. 41-55 ◽  
Author(s):  
WEI-LING CHIANG ◽  
CHENG-WU CHEN ◽  
FENG-HSIAG HSIAO
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Direct Method ◽  
Interconnected Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Fuzzy Models ◽  
Fuzzy Techniques ◽  
The Stability ◽  
Takagi Sugeno

This paper is concerned with the stability problem of nonlinear interconnected systems. Each of them consists of a few interconnected subsystems which are approximated by Takagi–Sugeno (T–S) type fuzzy models. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the asymptotic stability of interconnected systems. It is shown that the stability analysis problems of nonlinear interconnected systems can be reduced to linear matrix inequality (LMI) problems via suitable Lyapunov functions and T–S fuzzy techniques. Finally, numerical examples with simulations are given to demonstrate the validity of the proposed approach.

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

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.

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