A Unified Approach to High-Gain Adaptive Controllers

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-gain adaptive controllers achieve stability by automatically driving up the feedback gain monotonically. More recently, it was demonstrated that sample-and-hold implementations of the high-gain adaptive controller also require adaptation of the sampling rate. In this paper, we use recent advances in the mathematical field of dynamic equations on time scales to unify and generalize the discrete and continuous versions of the high-gain adaptive controller. We prove the stability of high-gain adaptive controllers on a wide class of time scales

Stability for time varying linear dynamic systems on time scales

AbstractWe study conditions under which the solutions of a time varying linear dynamic system of the form xΔ(t)=A(t)x(t) are stable on certain time scales. We give sufficient conditions for various types of stability, including Lyapunov-type stability criteria and eigenvalue conditions on “slowly varying'' systems that ensure exponential stability. Finally, perturbations of the unforced system are investigated, and an instability criterion is also developed

Nonregressivity

in switched linear circuits and mechanical systems