scholarly journals Stability Analysis for Linear Uncertain Switched Systems in Infinite-time Domain

2021 ◽  
Author(s):  
Yadong Shu ◽  
Bo Li
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Time Domain ◽  
Switched Systems ◽  
Uncertainty Theory ◽  
Switched System ◽  
Almost Sure Stability ◽  
Infinite Time ◽  
Internal Property ◽  
Stability Issues

Abstract In this work, an uncertain switched system expressed as a series of uncertain differential equations is considered in depth. Stability issues have been widely investigated on switched systems while few results related to stability analysis for uncertain switched systems can be found. Due to such fact, three different stabilities, including stability in measure, almost sure stability and stability in mean, are comprehensively studied for linear uncertain switched systems in infinite-time domain. Internal property of the systems is able to be illustrated from different perspectives with the help of above stability analysis. By employing uncertainty theory and the feature of switched systems, corresponding judgement theorems of these stabilities are proposed and verified. An example with respect to stability in measure is provided to display the validness of the results derived.

scholarly journals Stability Analysis for Autonomous Dynamical Switched Systems through Nonconventional Lyapunov Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
V. Nosov ◽  
J. A. Meda-Campaña ◽  
J. C. Gomez-Mancilla ◽  
J. O. Escobedo-Alva ◽  
R. G. Hernández-García
Keyword(s):  
Stability Analysis ◽  
Finite Number ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Switched System ◽  
Linear Functions ◽  
Asymptotically Stable ◽  
Multiple Lyapunov Functions ◽  
Stability Theorems ◽  
The Stability

The stability of autonomous dynamical switched systems is analyzed by means of multiple Lyapunov functions. The stability theorems given in this paper have finite number of conditions to check. It is shown that linear functions can be used as Lyapunov functions. An example of an exponentially asymptotically stable switched system formed by four unstable systems is also given.

scholarly journals A New Stability Analysis of Uncertain Delay Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Xiao Wang ◽  
Yufu Ning
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Almost Sure Stability ◽  
Delay Differential ◽  
The Relationship

This paper first provides a concept of almost sure stability for uncertain delay differential equations and analyzes this new sort of stability. In addition, this paper derives three sufficient conditions for uncertain delay differential equations being stable almost surely. Finally, the relationship between almost sure stability and stability in measure for uncertain delay differential equations is discussed.

scholarly journals Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time Subsystems

2007 ◽  
Vol 17 (4) ◽  
pp. 447-454 ◽  
Author(s):  
Guisheng Zhai ◽  
Xuping Xu ◽  
Hai Lin ◽  
Derong Liu
Keyword(s):  
Stability Analysis ◽  
Lie Algebra ◽  
Discrete Time ◽  
Continuous Time ◽  
Switched Systems ◽  
Switched System ◽  
Quadratic Lyapunov Function ◽  
Algebraic Stability ◽  
Arbitrary Switching ◽  
Exponentially Stable

Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time SubsystemsWe analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.

Observer Design and Stabilization for a Class of Switched System

2011 ◽  
Vol 422 ◽  
pp. 514-518
Author(s):  
Ming Yuan Shieh ◽  
Juing Shian Chiou
Keyword(s):  
Stability Analysis ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Switched System ◽  
Observer Design ◽  
Asymptotically Stable ◽  
Lyapunov Stability Theorem ◽  
State Transformation ◽  
Switching Law

This paper presents a novel and general approach, which is based on the Lyapunov stability theorem, to synthesize the observer and stabilization of the switched systems. On stability analysis, we can choose a particular state transformation matrix to transfer the observer-based switched system such that all subsystems can be decomposed into stable and unstable blocks. Some sufficient conditions are derived under a switching law such that the observer-based switched system is asymptotically stable. Finally, an example is presented to illustrate the proposed schemes.

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