Finite‐Time Stability and Stabilization of Linear Itô Stochastic Systems with State and Control‐Dependent Noise

In this paper, finite‐time stability and stabilization problems for a class of linear stochastic systems are studied. First, a new concept of finite‐time stochastic stability is defined for linear stochastic systems. Then, based on matrix inequalities, some sufficient conditions under which the stochastic systems are finite‐time stochastically stable are given. Subsequently, the finite‐time stochastic stabilization is studied and some sufficient conditions for the existence of a state feedback controller and a dynamic output feedback controller are presented by using a matrix inequality approach. An algorithm is given for solving the matrix inequalities arising from finite‐time stochastic stability (stabilization). Finally, two examples are employed to illustrate the results.