Donglei Fan

Donglei Fan, Danielle C. Tarraf

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.

Donglei Fan, Danielle C. Tarraf

We consider a class of systems over finite alphabets, namely discrete-time systems with linear dynamics and a finite input alphabet. We formulate a notion of finite uniform bisimulation, and motivate and propose a notion of regular finite uniform bisimulation. We derive sufficient conditions for the existence of finite uniform bisimulations, and propose and analyze algorithms to compute finite uniform bisimulations when the sufficient conditions are satisfied. We investigate the necessary conditions, and conclude with a set of illustrative examples.