Finite-time stability and stabilization of linear stochastic systems

This paper introduces a new finite-time stability concept for linear stochastic systems which is defined as finite-time stochastic (c₁, c₂)-stability. Some practical test criteria for finite-time stochastic (c₁, c₂)-stability are obtained. In the sequence, the finite-time stochastic (c₁, c₂)-stabilization is studied and some sufficient conditions are given via state-feedback using matrix inequality approach. An algorithm is presented for solving the matrix inequalities arising from finite-time stochastic (c₁, c₂)-stabilization. Finally, two examples are employed to illustrate the results.