The paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in (0,2) which involve a non-strict linear matrix inequality (LMI) method and a strict LMI method, respectively. The forms of non-strict and strict LMIs are brand-new and distinguished with the existing literature, which fill the gaps of studies for admissibility. These approaches are available to the order in (0,2) without separating the order ranges into (0,1) and [1,2). In addition, a method involved least real decision variables in terms of strict LMIs is derived which is more convenient to process the practical solution. Three numerical examples are given to illustrate the validity of proposed results.

Under the same seismic load, different local topography will have different effects, which is an important research field in seismic engineering. Hills are connected with valleys is a very typical terrain. Taking this terrain as an example, its response to the most destructive SH waves in the earthquake is studied. By simplifying and dividing the model, the wave functions satisfying the wave equation and boundary conditions in each region are constructed by using the complex function and moving coordinate method. The equations satisfying the boundary continuity conditions are established. With the help of calculation software, the numerical results are obtained. The influence of different parameters on ground motion is discussed.