String stability of infinite-dimension stochastic interconnected large-scale systems with time-varying delay

Abstract

The exponential string stability for a class of nonlinear interconnected large-scale systems with time-varying delay is analysed by using the box theory and constructing a vector Lyapunov function. Under the assumption that the time delay is bounded and continuous, a criterion for exponential string stability of the systems is obtained by analysing the stability of differential inequalities with time-varying delay. The large-scale system is exponential string stable when the conditions associating with the coefficient matrices of the system and the solutions of the Lyapunov equations, interconnected with the system, are satisfied. Since it is independent of the delays and simplifies the calculation, the criterion is easy to apply.

Stability of Infinite Dimensional Interconnected Systems with Impulsive and Stochastic Disturbances

“…From the properties of the operator (1) [25], we can take the expectation of inequality (12) and rewrite it as…”

“…Hence the vector Lyapunov function method is more efficient. The research team led by Professor Zhang has studied the stability of some infinite dimensional nonlinear interconnected systems with stochastic disturbances based on the vector Lyapunov function approach and obtained some important stability results; see [12][13][14].…”

“…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 , .…”

Exponential Mean‐Square Stability of Stochastic String Hybrid Systems Under Continuous Non‐Gaussian Excitation

“…We note that the criteria for exponential mean‐square stability of nonlinear continuous time stochastic string nonhybrid systems with parametric Gaussian white noises obtained by are not useful to study the stability of nonlinear with strong coupling interconnected systems. To omit this problem the vector Lyapunov function method (VLFM) was successfully used in . It seems to be an efficient mathematical tool in the study of stability of string systems.…”

“…A generalized version was proposed in . Next generalization of string stability for stochastic models with Gaussian excitation was given in . To find sufficient conditions of sting stability as well for deterministic models as for stochastic models, the Lyapunov function methods were used.…”