Analytical stability bound for a class of delayed fractional-order dynamic systems

Nonlinear Dynamics

Volumn 29, Issue 1-4, 2002, Pages 191-200

  Chen, Yangquan ^a   Moore, Kevin L ^a  

^a Utah State University   (United States)

Author keywords

Analytical solutions; Delay; Fractional order differentiator; Fractional order dynamic systems; Fractional order integrator; Lambert function; Stability bound

Indexed keywords

DELAY CONTROL SYSTEMS; DIFFERENTIAL EQUATIONS; FUNCTIONS; INTEGRATION; INVARIANCE; SYSTEM STABILITY;

DELAY DIFFERENTIAL EQUATIONS (DDE);

LINEAR CONTROL SYSTEMS;

EID: 0036650867     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016591006562     Document Type: Article

References (43)

1. A controller to overcome dead time
2. Control time-delay systems
3. Generalized Smith predictor for robust control of nuclear reactors with time delays
4. Iterative learning control for deterministic systems
5. Iterative learning control: Convergence, robustness and applications
6. Observationes varies in mathesin puram
7. Deformulis exponentialibus replicatis
8. De serie lambertina plurimistique eius insignibus proprietatibus
9. On the Lambert W function
10. Lambert's W function in Maple
11. A sequence of series for the Lambert W function
12. Some applications of the Lambert's W function to physics
13. The linear difference-differential equation with constant coefficients
14. Unwinding the branches of the Lambert W function
15. Analytical solution of a system of homogeneous delay differential equations via the Lambert function
16. Analytical stability bound for delayed second order systems with repeating poles using Lambert function w
17. Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations
18. On the appearance of the fractional derivative in the behavior of real materials
19. Application of fractional-order derivatives to calculation of heat load intensity change in blast furnace walls
20. The non-integer integral and its application to control systems
21. Fractional calculus applications in control systems
22. Stability result on fractional differential equations with applications to control processing
23. The Laplace transform method for linear differential equations of the fractional order
24. Analytic continuation of operators-operators acting complex s-time. Applications: From number theory and group theory to quantum field and string theories
25. Operator of fractional derivative in the complex plane
26. Control quality enhancement by fractional order controllers
27. State-space representation for fractional order controllers
28. The CRONE toolbox for Matlab
29. Discretization schemes for fractional order differentiators and integrators
30. Analytical stability bound for a class of delayed fractional-order dynamic systems
31. The frequency method for stability investigation of fractional control systems
32. The modelling and analysis of fractional-order control systems in frequency domain