Output Observability of Systems Over Finite Alphabets with Linear Internal Dynamics

TL;DR

This paper introduces new notions of output observability for systems over finite alphabets with linear dynamics, providing conditions, verification algorithms, and observer constructions for state estimation.

Contribution

It proposes three novel output observability concepts, along with necessary and sufficient conditions and algorithms for verification and observer design.

Findings

Derived conditions for output observability

Developed algorithms to verify observability conditions

Constructed finite memory output observers

Abstract

We consider a class of systems over finite alphabets with linear internal dynamics, finite-valued control inputs and finitely quantized outputs. We motivate the need for a new notion of observability and propose three new notions of output observability, thereby shifting our attention to the problem of state estimation for output prediction. We derive necessary and sufficient conditions for a system to be output observable, algorithmic procedures to verify these conditions, and a construction of finite memory output observers when certain conditions are met. We conclude with simple illustrative examples.