6 citations · 8 across the 2 of their papers we have counts for
5 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…
A Unified Floquet Theory for Discrete, Continuous, and Hybrid Periodic Linear Systems
Jeffrey J. DaCunha, John M. Davis
In this paper, we study periodic linear systems on periodic time scales which include not only discrete and continuous dynamical systems but also systems with a mixture of discrete…