Practical stability of large-scale uncertain control systems on time scales

Abstract

The theory of dynamical systems on time scales and Lyapunov theory are used to present a unified approach to the stabilization problem of nonlinear uncertain dynamical systems which encompasses both discrete and continuous cases. First, preliminary results on differential inequalities and existence of extremal solutions are established. These results are then used to prove several theorems pertaining to the practical stability of dynamical systems on time scales. As an application, a special class of large-scale uncertain control systems is considered and an example is given.

AMS Nos.:

• 34D20
• 34H05
• 39A11
• 58F10

Keywords:

• Practical stability
• Lyapunov stability
• uncertain systems
• discrete systems
• control systems

^∗Work supervised by Dr. Lakshmikantham

^∗Work supervised by Dr. Lakshmikantham

Notes

^∗Work supervised by Dr. Lakshmikantham