No abstract

This paper addresses the problem of stability in terms of two measures for impulsive switched nonlinear systems. By using multiple Lyapunov functions (MLFs), we establish some sufficient conditions of all kinds of stability in terms of two measures for impulsive switched nonlinear systems. Moreover, the derivatives of MLF in our results only satisfy the corresponding conditions in a circular region.Meanwhile, the proposed results also improve the related existing results on the same topic by removing some restrictive conditions. Finally, some illustrative examples are presented to verify the validity of our proposed methods.

This paper addresses the regional stability problem for impulsive switched nonlinear systems (ISNSs) whose subsystems have more than one equilibrium point, that is, multiple equilibrium points (MEPs) coexist. Meanwhile, we derive analytical results and sufficient conditions about the regional stability. Through investigating the dynamical behavior of ISNSs with MEPs, the multiple Lyapunov functions (MLFs) method is established for the regional stability. It is shown that main results obtained in this paper not only guarantee the regional stability of ISNSs with MEPs under arbitrary switching signals but also provide a new method to determine the corresponding stable regions for the regional stability. Numerical simulations are given to illustrate and verify advantages of our proposed results.

The smart classroom with the support of interactive media can effectively integrate resources, reshape the ecological environment of teaching and optimize classroom teaching and learning. New changes occur to the learning features and learning organization of the interactive mediasupported smart classroom when compared with the traditional multimedia classroom. In this paper, by video recording of classroom instructions, a comparison is made between the smart classroom teaching supported by interactive media and the traditional multimedia classroom teaching, applying the methods of interactive analysis and S-T analysis, utilizing Nvivo software to assist recording. The results show that, in comparison with the traditional multimedia classroom, the smart classroom supported by interactive media is more learner-centric and thus being conducive to students' subjectivity and make their participation in learning activities more abundant and deeper.