Analysis of a Class of Fractional Nonlinear Multidelay Differential Systems
Open Access
- 15 October 2017
- journal article
- research article
- Published by Hindawi Limited in Discrete Dynamics in Nature and Society
- Vol. 2017, 1-15
- https://doi.org/10.1155/2017/9050289
Abstract
We address existence and Ulam-Hyers and Ulam-Hyers-Mittag-Leffler stability of fractional nonlinear multiple time-delays systems with respect to two parameters’ weighted norm, which provides a foundation to study iterative learning control problem for this system. Secondly, we design PID-type learning laws to generate sequences of output trajectories to tracking the desired trajectory. Two numerical examples are used to illustrate the theoretical results.Keywords
Funding Information
- National Natural Science Foundation of China (11661016, (2016)4006, [2015]7640, [2015]003, 11671339)
This publication has 42 references indexed in Scilit:
- Stability analysis of impulsive functional systems of fractional orderCommunications in Nonlinear Science and Numerical Simulation, 2014
- E α -Ulam type stability of fractional order ordinary differential equationsJournal of Applied Mathematics and Computing, 2013
- Ulam’s type stability of impulsive ordinary differential equationsJournal of Mathematical Analysis and Applications, 2012
- Nonlinear impulsive problems for fractional differential equations and Ulam stabilityComputers & Mathematics with Applications, 2012
- Convergence characteristics of proportional-type iterative learning control in the sense of Lebesgue-p normIET Control Theory & Applications, 2012
- Analysis of nonlinear fractional control systems in Banach spacesNonlinear Analysis, 2011
- Iterative learning control design of nonlinear multiple time-delay systemsApplied Mathematics and Computation, 2011
- A survey on iterative learning control for nonlinear systemsInternational Journal of Control, 2011
- PD-Type iterative learning control for nonlinear time-delay system with external disturbanceJournal of Systems Engineering and Electronics, 2006
- Bettering operation of Robots by learningJournal of Robotic Systems, 1984