67 citations · 77 across the 4 of their papers we have counts for
4 papers
Linear State Feedback Stabilization on Time Scales
Billy J. Jackson, John M. Davis, Ian A. Gravagne +1
For a general class of dynamical systems (of which the canonical continuous and uniform discrete versions are but special cases), we prove that there is a state feedback gain such…
Algebraic and Dynamic Lyapunov Equations on Time Scales
John M. Davis, Ian A. Gravagne, Robert J. Marks +1
We revisit the canonical continuous-time and discrete-time matrix algebraic and matrix differential equations that play a central role in Lyapunov based stability arguments. The go…
Controllability, Observability, Realizability, and Stability of Dynamic Linear Systems
John M. Davis, Ian A. Gravagne, Billy J. Jackson +1
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonun…
A Unified Approach to High-Gain Adaptive Controllers
Ian A. Gravagne, John M. Davis, Jeffrey J. DaCunha
It has been known for some time that proportional output feedback will stabilize MIMO, minimum-phase, linear time-invariant systems if the feedback gain is sufficiently large. High…