Observer synthesis for Linear Hybrid Systems with constrained discrete dynamics

A Linear Hybrid System (LHS) is defined as a collection of Linear Systems (LS's) and a switching signal determining, at each time, the LS structure that rules the behaviour of the LHS. These systems are being used to successfully represent different kinds of engineering systems. This work proposes an observer scheme for Linear Hybrid Systems (LHS's) where the switching signal is unknown but it can be represented by a discrete event machine like automata, Petri nets, etc. The proposed observer structure takes advantage of the general observability characterization presented in Vázquez et al. (2015), where neither the observability of the discrete event machine nor the observabilities of the linear systems are required. First, the observer scheme estimates the discrete location, which is also named discrete state, by combining information from the continuous and discrete outputs. Next, the observer structure estimates the continuous state based on the knowledge of the visited locations, i.e., the discrete state trajectory. The observer scheme is flexible, allowing the use of different types of observers for the continuous and discrete states.