TIME-VARYING LYAPUNOV FUNCTIONS AND LYAPUNOV
STABILITY OF NONAUTONOMOUS FRACTIONAL
ORDER SYSTEMS
Bichitra Kumar Lenka
Department of Mathematics and Statistics
Indian Institute of Science Education and Research Kolkata
Nadia, West Bengal 741246, INDIA
We present a new inequality which involves the Caputo fractional derivative of the product of two continuously differentiable functions, and establish its various properties. The inequality and its properties enable us to construct potential time-varying Lyapunov functions for the Lyapunov stability analysis of fractional order systems. We use time-varying Lyapunov functions to analyse the stability of nonautonomous fractional order systems. By considering time-varying quadratic Lyapunov function, we establish new stability conditions for certain class of nonautonomous fractional order systems where the fractional order lies between and .
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