Time-varying Lyapunov functions for nonautonomous nabla fractional order systems
1School of Mathematics, Southeast University, Nanjing, 211189, China.
Abstract:
The classical Leibniz rule for the integer difference cannot be easily applicable for the fractional counterpart. It further leads to a great difficulty in the calculation of the Lyapunov functions with product form. To overcome such a challenge, several fractional difference inequalities are developed for Lyapunov functions which are the product of a time sequence and a function regarding to system state. To further enrich the design of time-varying Lyapunov function, the differentiable convex condition is introduced and then three elegant inequalities are derived. Those inequalities hold for the Caputo/Riemann-Liouville/Grünwald-Letnikov definitions which bring the possibility of the Lyapunov stability analysis for nonautonomous nabla fractional order systems. Finally, illustrative examples serve to illustrate the applicability and practicability of the theoretical results.
Related Concept Videos
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Feedback control systems
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
First Order Systems
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
Linear time-invariant Systems
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
Second Order systems II

