Stabilization for a class of stochastic nonlinear systems with arbitrary switching via the common Lyapunov function method

2013 ◽  
Vol 11 (5) ◽  
pp. 926-937 ◽  
Author(s):  
Jian Wu ◽  
Weisheng Chen ◽  
Jing Li ◽  
Wenlong Ren
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Function Method ◽  
Stochastic Nonlinear Systems ◽  
Common Lyapunov Function ◽  
Arbitrary Switching ◽  
Lyapunov Function Method ◽  
The Common

scholarly journals Pinning Synchronization of Switched Complex Dynamical Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Liming Du ◽  
Feng Qiao ◽  
Fengying Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Function Method ◽  
Complex Dynamical Networks ◽  
Switching Topology ◽  
Dynamical Networks ◽  
Switching Law ◽  
Arbitrary Switching ◽  
Lyapunov Function Method ◽  
Networks With Switching Topology

Network topology and node dynamics play a key role in forming synchronization of complex networks. Unfortunately there is no effective synchronization criterion for pinning synchronization of complex dynamical networks with switching topology. In this paper, pinning synchronization of complex dynamical networks with switching topology is studied. Two basic problems are considered: one is pinning synchronization of switched complex networks under arbitrary switching; the other is pinning synchronization of switched complex networks by design of switching when synchronization cannot achieved by using any individual connection topology alone. For the two problems, common Lyapunov function method and single Lyapunov function method are used respectively, some global synchronization criteria are proposed and the designed switching law is given. Finally, simulation results verify the validity of the results.

scholarly journals Second-Order Consensus for Multiagent Systems under Directed and Switching Topologies

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Lixin Gao ◽  
Jingjing Zhang ◽  
Wenhai Chen
Keyword(s):  
Function Method ◽  
Sufficient Conditions ◽  
Common Lyapunov Function ◽  
Special Cases ◽  
Lyapunov Function Method ◽  
Leader Following ◽  
The Common ◽  
Feedback Laws ◽  
Integrator Model ◽  
Double Integrator

We consider multiagent consensus problems in a decentralized fashion. The interconnection topology among the agents is switching and directed. The agent dynamics is expressed in the form of a double-integrator model. Two different cases are considered: one is the leader-following case and the other is the leaderless case. Based on graph theory and the common Lyapunov function method, some sufficient conditions are established for the consensus stability of the considered systems with the neighbor-based feedback laws in both leader-following case and leaderless case, respectively. As special cases, the consensus conditions for balanced and undirected interconnection topology cases can be established directly. Finally, two numerical examples are given to illustrate the obtained results.

Adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics

2021 ◽  
pp. 014233122098563
Author(s):  
Fei Shen ◽  
Xinjun Wang ◽  
Xinghui Yin
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Dead Zone ◽  
Small Neighborhood ◽  
Unmodeled Dynamics ◽  
Stochastic Nonlinear Systems ◽  
Dynamic Surface ◽  
Barrier Lyapunov Function ◽  
Full State

This paper investigates the problem of adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics. To stabilize such a system, a dynamic signal is introduced to dominate unmodeled dynamics and an assistant signal is constructed to compensate for the effect of the dead zone. Dynamic surface control is used to solve the “complexity explosion” problem in traditional backstepping design. Two cases of symmetric and asymmetric Barrier Lyapunov functions are discussed respectively in this paper. The proposed Barrier Lyapunov function based on backstepping method can ensure that the output tracking error converges in the small neighborhood of the origin. This control scheme can ensure that semi-globally uniformly ultimately boundedness of all signals in the closed-loop system. Two simulation cases are proposed to verify the effectiveness of the theoretical method.

Robust stability and memory state feedback control for a class of switched nonlinear systems with multiple time-varying delays

2021 ◽  
pp. 107754632098598
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Multiple Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Common Lyapunov Function ◽  
Suggested Approach ◽  
Aggregation Techniques

This study is concerned with the stability analysis and the feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Unusually, more general time delays, which depend on the subsystem number, are considered. In this regard, by constructing a novel common Lyapunov function, using the aggregation techniques and the Borne and Gentina criterion, new algebraic stability and feedback stabilization conditions under arbitrary switching are derived. The proposed results are explicit and obtained without searching a common Lyapunov function through the linear matrix inequalities approach, considered a difficult matter in this case. At last, two numerical simulation examples are shown to prove the practical utility of the suggested approach.

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