Abstract
This paper discusses from the algebraic points of view the relationship among the four properties of discretetime piecewise linear systems, that is, observability, determinability, mode estimatability, and mode-sequence estimatability. First, necessary and sufficient conditions for the system to be determinable, and to be modesequence estimatable are derived. Next, the observability property is characterized in terms of those conditions. Finally, the relationship between the observability property of the original system and the well-posedness property of the time-reversed system is discussed.
