David L. Elliott

Exponential observers for nonlinear dynamic systems

An observer theory is presented for nonlinear dynamic systems in this paper. Exponential observers are defined (asymptotic state estimators with exponentially decaying error). A Lyapunov-like method is introduced for the design of exponential observers. Two theorems are presented to give conditions on the system structure such that there exists an exponential observer for the given system.

Observability of Nonlinear Systems

The purpose of this paper is to investigate the problem of observability of nonlinear systems. Two sufficient conditions of global observability of nonlinear systems are presented: (1) the ratio condition which is the generalization of Fujisawa and Kuhs (1971) ratio condition of circuit theory, (2) the strongly positive semidefinite condition. The relationships between these two conditions as well as the condition of positive definiteness of Fitts (1970) are given.

Global state and feedback equivalence of nonlinear systems

The problem of finding global state space transformations and global feedback of the form u(t)= α(x) + ν(t) to transform a given nonlinear system xdot= f(x)+ g(x)u to a controllable linear system on Rn or on an open subset of Rn, is considered here. We give a complete set of differential geometric conditions which are equivalent to the existence of a solution to the above problem.

Controllability of Bilinear Systems

The systems we study are homogeneous bilinear, single-input:

Ambiguous Behavior of Logic Bistable Systems

\dot{x}=(A+{{u}_{t}}B)x

A controllability counterexample

(1.1)

Diffusions on Manifolds Arising from Controllable Systems

{{x}_{k+1}}=(A+{{u}_{k}}B){{x}_{k}}