Some Differential Inequalities on Time Scales and Their Applications to Feedback Control Systems

Abstract

This paper deals with feedback control systems on time scales. Firstly, we generalize the semicycle concept to time scales and then establish some differential inequalities on time scales. Secondly, as applications of these inequalities, we study the uniform ultimate boundedness of solutions of these systems. We give a new method to investigate the permanence of ecosystem on time scales. And some known results have been generalized. Finally, an example is given to support the result.

Dynamic behaviors for a delay Lasota–Wazewska model with feedback control on time scales

“…There has been considerable work done on the study of the almost periodicity and stability of the systems on time scales. Many interesting and important results can be found in many articles; for example, see [2][3][4][5][6][7][8][9][10] and the references cited therein.…”

“…The feedback control models play an important and fundamental role. We also refer to Fan [7], Chen [12], Li [13] and [14][15][16][17][18][19][20][21][22] for further study on systems with feedback control.…”

“…The permanence of ecosystems will play an important role to predict the change trend of populations in the long run. Many authors [7,12,21,29,30] have investigated the permanence of biological systems. However, to the best of the authors' knowledge, to this day, still no scholars consider the permanence of the Lasota-Wazewska model with feedback control on time scales.…”