Sensitivity analysis of nonlinear fractional order control systems with state delay

Abstract

In this paper, we consider a class of nonlinear fractional order control system with delay in state variable. Existence and uniqueness of solution are shown by using method of steps. The sensitivity of the state and control with respect to the parameters of the system is shown. Finally, analytical results are substantiated by numerical examples.

Keywords:

• fractional derivatives and integrals
• Mittag–Leffler type functions
• fractional differential equations
• sensitivity
• nonlinear systems

2010 AMS Subject Classification:

• 26A33
• 33E12
• 34A08
• 93B35
• 93C10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author would like to thank Ministry of Human Resource Development, Government of India [Grant No. MHR02-23-200-429] for the financial support.