A new approach to the theory of the stability of linear canonical systems of differential equations with periodic coefficients

2004 ◽  
Vol 68 (2) ◽  
pp. 183-198 ◽  
Author(s):  
A.A. Zevin
Keyword(s):  
Differential Equations ◽  
Periodic Coefficients ◽  
New Approach ◽  
Canonical Systems ◽  
Systems Of Differential Equations ◽  
The Stability

scholarly journals On the Stability of Linear Canonical Systems with Periodic Coefficients

1966 ◽  
Vol 6 (2) ◽  
pp. 256-256 ◽  
Author(s):  
W. A. Coppel ◽  
A. Howe
Keyword(s):  
Closed Curve ◽  
Mathematical Society ◽  
Periodic Coefficients ◽  
Canonical Systems ◽  
Australian Mathematical Society ◽  
The Stability

Journal of the Australian Mathematical Society 5 (1965), 169–195Theorem 9 (p. 183) should read: The indices of any closed curve inD have the formn+ = hp/s, n− = hq/sfor some integer h, where s (1 ≦ s ≦ n) is the largest number of identical blocks into which the signature σ can be partitioned. Moreover, for any integer h there exists a closed curve in d with these indices.

Galerkin Approximations for Stability of Delay Differential Equations With Time Periodic Coefficients

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Anwar Sadath ◽  
C. P. Vyasarayani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Approximate Model ◽  
Periodic Coefficients ◽  
Galerkin Approximations ◽  
Approximate System ◽  
The Stability ◽  
Delay Differential ◽  
Time Periodic ◽  
Least Squares Approach

A numerical method to determine the stability of delay differential equations (DDEs) with time periodic coefficients is proposed. The DDE is converted into an equivalent partial differential equation (PDE) with a time periodic boundary condition (BC). The PDE, along with its BC, is then converted into a system of ordinary differential equations (ODEs) with time periodic coefficients using the Galerkin least squares approach. In the Galerkin approach, shifted Legendre polynomials are used as basis functions, allowing us to obtain explicit expressions for the approximate system of ODEs. We analyze the stability of the discretized ODEs, which represent an approximate model of the DDEs, using Floquet theory. We use numerical examples to show that the stability charts obtained with our method are in excellent agreement with those existing in the literature and those obtained from direct numerical simulation.

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