An improved sufficient condition for absence of limit cycles in digital filters
Palghat P. Vaidyanathan, V. Liu · IEEE Transactions on Circuits and Systems · 1987
It is known that if the state transition matrix A of a digital filter structure is such thatD - A^{\dagger}DAis positive definite for some diagonal matrixDof positive elements, then all zero-input limit cycles can be suppressed. This paper shows that positive semidefiniteness ofD - A^{\dagger}DAis in fact sufficient. As a result, it is now possible to explain the absence of limit cycles in Gray-Markel lattice structures based only on the state-space viewpoint.