Stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple Lyapunov functions

@article{Chatterjee2006StabilityAO,
  title={Stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple Lyapunov functions},
  author={Debasish Chatterjee and Daniel Liberzon},
  journal={SIAM J. Control. Optim.},
  year={2006},
  volume={45},
  pages={174-206}
}
This paper presents a general framework for analyzing stability of nonlinear switched systems, by combining the method of multiple Lyapunov functions with a suitably adapted comparison principle in the context of stability in terms of two measures. For deterministic switched systems, this leads to a unification of representative existing results and an improvement upon the current scope of the method of multiple Lyapunov functions. For switched systems perturbed by white noise, we develop new… 
View via Publisher
liberzon.csl.illinois.edu
145 Citations
Highly Influential Citations
8
Background Citations
47
Methods Citations
30
Results Citations
5

145 Citations

Asymptotic Stability Analysis for Switched Stochastic Nonlinear Systems Using Mode-dependent Uniformly Stable Functions

In this paper, we intend to investigate uniform global asymptotic stability in probability (UGAS-P) for a class of time-varying switched stochastic nonlinear systems. Conventional criteria on…

Asymptotic Stability Analysis for Switched Stochastic Nonlinear Systems Using Mode-dependent Uniformly Stable Functions

In this paper, we intend to investigate uniform global asymptotic stability in probability (UGAS-P) for a class of time-varying switched stochastic nonlinear systems. Conventional criteria on…

On exponential stability for linear switched stochastic systems: Multiple Lyapunov functions approach

We are interested in characterizing the effect of noise perturbation on the stability of switched systems. To this end, we extend the multiple Lyapunov functions approach to the linear Itô stochastic…

On Stability of a Class of Switched Nonlinear Systems Subject to Random Disturbances

This paper addresses the stability problem for a class of switched nonlinear systems subject to random disturbances whose τ-order moments (τ > 1) are finite by using the average dwell-time approach to study the noise-to-state stability, the eλt-weighted (integral) noise- to- state stability and the global asymptotic stability of random switched systems.

Global exponential stability of switched systems

This paper proposes a method for the stability analysis of deterministic switched systems. Two motivational examples are introduced (nonholonomic system and constrained pendulum). The finite…

Stability of stochastic nonlinear switching systems

In this paper, the problem of stability on stochastic systems with state-dependent switching is investigated. To analyze properties of the switched system by means of Itô's formula and Dynkin's…

Analysis of Stability and Robust Stabilization for Impulsive Switched Stochastic Systems

Many practical systems in physics, biology, engineering, and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. In…

Lyapunov Conditions for Stability of Stochastic Impulsive Switched Systems

  • W. RenJ. Xiong
  • Mathematics
    IEEE Transactions on Circuits and Systems I: Regular Papers
  • 2018
General Lyapunov function and fixed dwell-time are implemented in this paper to analyze input-to-state stability and global stability of stochastic impulsive switched systems.

Multiple switching-time-dependent discretized Lyapunov functions/functionals methods for stability analysis of switched time-delay stochastic systems

Stability of a class of stochastic switched systems with time delays

In this paper, the problem of stochastic switched systems with time delay is investigated. To study the existence of the solution to the switched system with time delay by means of Ito's formula, it…
...

46 References

Multiple Lyapunov functions and other analysis tools for switched and hybrid systems

Bendixson's theorem is extended to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of "continuous switched" systems.

The stability analysis of switched systems

The concepts of attractive region and semi-attractive region are proposed and used as a tool for analyzing the Lyapunov stability of switched systems and are more practical than the other presented ones.

Lyapunov-like techniques for stochastic stability

  • P. Florchinger
  • Mathematics
    Proceedings of 1994 33rd IEEE Conference on Decision and Control
  • 1994
The purpose of this paper is to give a survey of the results proved in Florchinger (1993) concerning the stabilizability problem for control stochastic nonlinear systems driven by a Wiener process.…

Uniform stability of switched linear systems: extensions of LaSalle's Invariance Principle

  • J. Hespanha
  • Mathematics
    IEEE Transactions on Automatic Control
  • 2004
This paper provides a collection of results that can be viewed as extensions of LaSalle's Invariance Principle to certain classes of switched linear systems that can deduce asymptotic stability using multiple Lyapunov functions whose Lie derivatives are only negative semidefinite.

Dwell-time controllers for stochastic systems with switching Markov chain

Stability and robustness for hybrid systems

Stability and robustness issues for hybrid systems are considered in this paper. Present stability results, that are extensions of classical Lyapunov theory, are not straightforward to apply in…

Optimal practical stabilization and controllability of systems with Markovian jumps

A Smooth Converse Lyapunov Theorem for Robust Stability

This paper presents a converse Lyapunov function theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems.…

Finite-Time Stability of Continuous Autonomous Systems

It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related and converse Lyap Unov results can only assure the existence of continuous Lyap unov functions.

On Input-to-State Stability of Impulsive Systems

This paper introduces appropriate concepts of input-to-state stability (ISS) and integral-ISS for systems with impulsive effects. We provide a set of Lyapunov-based sufficient conditions to establish…