Comparison principle and stability of impulsive stochastic functional differential systems in terms of two measures

Stability of Infinite Dimensional Interconnected Systems with Impulsive and Stochastic Disturbances

“…In the real industries, the control problem of many complex dynamic systems can be translated into the stability analysis. At present, there have been lots of research results about the stability analysis for the finite dimensional interconnected systems; see [1][2][3][4][5][6][7][8][9][10][11]. Nevertheless, considering that the connections or disconnections between the subsystems of the real interconnected systems are uncertain, which means that the dimension of the interconnected systems is uncertain, the interconnected systems can be described by infinite dimensional equations.…”

“…On the other hand, there are some unavoidable disturbances in the real systems, such as stochastic disturbance and impulsive disturbance. Therefore some researchers have given stability analysis for some finite dimensional complex dynamic systems with impulsive and stochastic disturbances; see [6][7][8][9][10][11].…”

“…The applied methods presented in [1][2][3][4][5][6][7][8][9][10][11] are based on the scalar Lyapunov function approach or the LMI tool. In fact, the LMI method is essentially a kind of the method using the scalar Lyapunov function method.…”

“…The obtained stability results in [2][3][4][5][6][7][8][9][10][11][12]14] are focused on the stability of the steady state of the systems without considering the size relationship of the state variables when the systems converge to steady-state process. For example, considering interconnected systeṁ= ( , ) (here = col( 1 , 2 , .…”