Non-fragile Finite-time Stabilization for Discrete Mean-field Stochastic Systems

TL;DR

This paper addresses the challenge of stabilizing linear discrete mean-field stochastic systems within finite time, considering control uncertainties modeled by Bernoulli distributions, and introduces a novel state transition matrix approach.

Contribution

It proposes a new state transition matrix method and derives necessary and sufficient conditions for non-fragile finite-time stabilization of stochastic systems.

Findings

Derived new stabilization conditions for uncertain stochastic systems.

Validated the approach with a practical example.

Contributed to finite-time control theory with Lyapunov theorems.

Abstract

In this paper, the problem of non-fragile finite-time stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli distribution. A new approach called the ``state transition matrix method" is introduced and some necessary and sufficient conditions are derived to solve the underlying stabilization problem. The Lyapunov theorem based on the state transition matrix also makes a contribution to the discrete finite-time control theory. One practical example is provided to validate the effectiveness of the newly proposed control strategy.