Finite-time stability and stabilization of nonlinear stochastic hybrid systems

Abstract

This paper deals with the problem of finite-time stability and stabilization of nonlinear Markovian switching stochastic systems which exist impulses at the switching instants. Using multiple Lyapunov function theory, a sufficient condition is established for finitetime stability of the underlying systems. Furthermore, based on the state partition of continuous parts of systems, a feedback controller is designed such that the corresponding impulsive stochastic closed-loop systems are finite-time stochastically stable. A numerical example is presented to illustrate the effectiveness of the proposed method.

Finite-Time Regional Verification of Stochastic Nonlinear Systems

“…Both here and in [18,27] the results should be extendable to the case where the noise is a mixture of Gaussians and discrete switches (in the DT case) or a mixture of Wiener and Poisson processes (in the CT case). This is a fairly common form for noise models, although sometimes more complicated noise models are considered, such as Gaussian noise filtered through a nonlinear function [4].…”

“…Recall that we are interested in the infinitesimal operator A B(x, t) defined in Equation 1. For systems of the form dx(t) = f (x)dt + g(x)dw(t), we can compute [27] A B(x, t) = ∂B ∂t…”

“…Much of the continuous-state verification research has focused on nonlinear systems with Gaussian noise [18,27], which we continue to focus on in this paper. Both here and in [18,27] the results should be extendable to the case where the noise is a mixture of Gaussians and discrete switches (in the DT case) or a mixture of Wiener and Poisson processes (in the CT case).…”

Finite-time regional verification of stochastic non-linear systems

“…Recall that we are interested in the infinitesimal operator A B(x, t) defined in Equation 1. For systems of the form dx(t) = f (x)dt + g(x)dw(t), we can compute [28] A B(x, t) = ∂B ∂t…”

Robust and Resilient Finite-Time Control of a Class of Discrete-Time Nonlinear Systems

“…Yang, et al (2009) consider nonlinear systems that are hybrid and stochastic. Other works have studied the FTS of nonlinear quadratic systems (Amato, et al, 2010b).…”