the rock masses in a construction site of underground cavern are generally not continuous, due to the presence of discontinuities, such as bedding, joints, faults, and fractures. the performance of an underground cavern is principally ruled by the mechanical behaviors of the discontinuities in the vicinity of the cavern. during underground excavation, many surrounding rock failures have close r...

We consider an integral variational control system on a Banach space X and we study the connections between its uniform exponential stability and the I R , X , O R , X stability, where I andO are Banach function spaces. We identify the viable classes of input spaces and output spaces related to the exponential stability of systems and provide optimization techniques with respect to the input sp...

A framework of a general type of Petrovsky equation is formulated. The characteristic equation for eigenvalues of the system is derived and the associated eigenfunctions are found. For N connected beams with linear feedbacks at joint points, the asymptotic expansions of eigenvalues and eigenfunctions are further developed, and the Riesz basis property and the exponential stability are then conc...

In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of discrete Hopfield neural networks with delays. Some new stability criteria for system are derived by using the Lyapunov functional method and the linear matrix inequality approach, for estimating the upper bound of Lyapunov functional derivative. ...

Keywords: Differential equations Difference equations Stability Bohl–Perron theorem Linear delay dynamic equations Time scales Uniform exponential stability a b s t r a c t This paper is concerned with the uniform exponential stability of ordinary and delay dynamic equations. After revealing the equivalence between various types of uniform exponential stability definitions on time scales with b...

This paper address the exponential stability for a class of switched systems with mixed time delays. Based on linear matrix inequalities and Lyapunov-Krasovskii functional approach, a geometrically switching rule for the exponential stability of the system is designed. The approach allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. ...

The rock masses in a construction site of underground cavern are generally not continuous, due to the presence of discontinuities, such as bedding, joints, faults, and fractures. The performance of an underground cavern is principally ruled by the mechanical behaviors of the discontinuities in the vicinity of the cavern. During underground excavation, many surrounding rock failures have close r...