Linear Approach for Synchronous State Stability in Fully Connected PLL Networks

Table 1

Eigenvalues for an 𝑁-node network.

𝑛	Eigenvalues and multiplicities
	Polynomial	𝜆1	𝑚	𝜆2	𝑚
2	(𝜆^2+𝜇1𝜆+2𝑘)	−𝜇12+𝜇^21−8𝑘2	1	−𝜇12−𝜇^21−8𝑘2	1
3	(𝜆^2+𝜇1𝜆+3𝑘)^2	−𝜇12+𝜇^21−12𝑘2	2	−𝜇12−𝜇^21−12𝑘2	2
4	(𝜆^2+𝜇1𝜆+4𝑘)^3	−𝜇12+𝜇^21−16𝑘2	3	−𝜇12−𝜇^21−16𝑘2	3
5	(𝜆^2+𝜇1𝜆+5𝑘)^4	−𝜇12+𝜇^21−20𝑘2	4	−𝜇12−𝜇^21−20𝑘2	4
6	(𝜆^2+𝜇1𝜆+6𝑘)^5	−𝜇12+𝜇^21−246𝑘2	5	−𝜇12−𝜇^21−24𝑘2	5
7	(𝜆^2+𝜇1𝜆+7𝑘)^6	−𝜇12+𝜇^21−28𝑘2	6	−𝜇12−𝜇^21−28𝑘2	6
⋮	⋮	⋮	⋮	⋮	⋮
𝑁	(𝜆^2+𝜇1𝜆+𝑁𝑘)^(𝑁−1)	−𝜇12+𝜇^21−4𝑁𝑘2	(𝑁−1)	−𝜇12−𝜇^21−4𝑁𝑘2	(𝑁−1)