Necessary and sufficient conditions for input-output finite-time stability of impulsive dynamical systems

2015 ◽  
Author(s):  
F. Amato ◽  
G. De Tommasi ◽  
A. Pironti
Keyword(s):  
Dynamical Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Input Output ◽  
Time Stability ◽  
Finite Time Stability ◽  
Necessary And Sufficient

scholarly journals On necessary and sufficient conditions for output finite-time stability

Automatica ◽  
2021 ◽  
Vol 125 ◽  
pp. 109427
Author(s):  
Konstantin Zimenko ◽  
Denis Efimov ◽  
Andrey Polyakov ◽  
Artem Kremlev
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Time Stability ◽  
Finite Time Stability ◽  
Necessary And Sufficient

scholarly journals Sufficient Conditions for Finite-Time Stability of Impulsive Dynamical Systems

2009 ◽  
Vol 54 (4) ◽  
pp. 861-865 ◽  
Author(s):  
R. Ambrosino ◽  
F. Calabrese ◽  
C. Cosentino ◽  
G. De Tommasi
Keyword(s):  
Dynamical Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Time Stability ◽  
Finite Time Stability

Finite-Time Stabilization of Large-Scale Impulsive Dynamical Systems

2011 ◽  
Author(s):  
Wassim M. Haddad ◽  
Sergey G. Nersesov
Keyword(s):  
Dynamical Systems ◽  
Finite Time ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Time Stability ◽  
Finite Time Stability ◽  
Lipschitz Continuous ◽  
Time Dynamics ◽  
Stabilizing Controllers ◽  
System States

This chapter describes sufficient conditions for finite-time stability of nonlinear impulsive dynamical systems. For impulsive dynamical systems, it may be possible to reset the system states to an equilibrium state, in which case finite-time convergence of the system trajectories can be achieved without the requirement of non-Lipschitzian dynamics. Furthermore, due to system resettings, impulsive dynamical systems may exhibit non-uniqueness of solutions in reverse time even when the continuous-time dynamics are Lipschitz continuous. The chapter presents stability results using vector Lyapunov functions wherein finite-time stability of the impulsive system is guaranteed via finite-time stability of a hybrid vector comparison system. These results are used to develop hybrid finite-time stabilizing controllers for impulsive dynamical systems. Decentralized finite-time stabilizers for large-scale impulsive dynamical systems are also constructed. Finally, it gives a numerical example to illustrate the utility of the proposed framework.

Input–output finite time stability of fractional order linear systems with 0 < α < 1

2015 ◽  
Vol 39 (5) ◽  
pp. 653-659 ◽  
Author(s):  
Ya-jing Ma ◽  
Bao-wei Wu ◽  
Yue-E Wang ◽  
Ye Cao
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Linear Time ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Input Output ◽  
Time Stability ◽  
Caputo Fractional Derivatives ◽  
Order Linear ◽  
Finite Time Stability

The input–output finite time stability (IO-FTS) for a class of fractional order linear time-invariant systems with a fractional commensurate order 0 < α < 1 is addressed in this paper. In order to give the stability property, we first provide a new property for Caputo fractional derivatives of the Lyapunov function, which plays an important role in the main results. Then, the concepts of the IO-FTS for fractional order normal systems and fractional order singular systems are introduced, and some sufficient conditions are established to guarantee the IO-FTS for fractional order normal systems and fractional order singular systems, respectively. Finally, the state feedback controllers are designed to maintain the IO-FTS of the resultant fractional order closed-loop systems. Two numerical examples are provided to illustrate the effectiveness of the proposed results.

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