Stability regions
Stability regions
AAU
For a linear d-dimensional time-invariant dynamic equation
the stability region is given by
and determines the subset of the complex plane in which the spectrum of A is contained in order to guarantee exponential stability.
The classical cases are
Ordinary differential equations:
negative half plane
Difference equations:
unit circle with center -1
Hybrid equations:
Constant step-sizes:
continuous transition between the difference and differential equations case in the limit as h tends to 0.
Stability regions for dynamic equations on time scales
(cf. Pötzsche, Siegmund and Wirth: A spectral characterization of linear time-invariant systems on time scales, Discrete and Continuous Dynamical Systems (Series A) 9(5), 1223-1241, 2003)
Christian Pötzsche (Feb 2011)