Rank Conditions Of Observability Of Linear Hybrid DAS

A linear hybrid differential algebraic system (linear hybrid system in short) has much practical application. Observability is one of the most important properties of a linear hybrid system. There are two kind of methods in the research of linear system’s observability because the coefficient matrix (square matrix) of the state variables’differential function has two forms:invertible matrix and singular matrix. Researchers often use observability matrix’s rank and generalized inverse of matrix for the first case, while observable spaces’ operation and impulses are used for the second case, which is complicated and more difficult to understand.In this thesis, we transform a linear hybrid system whose coefficient matrix of the state variables’ differential function is singular into another linear hybrid system whose coefficient matrix is invertible, in order to discuss rank conditions of observability of linear hybrid system.The thesis is organized as follows:some background knowledge is given in Chapter1. Chapter2includes preliminaries. In Chapter3, the first thing we do is transforming a linear hybrid system whose coefficient matrix of the state variables’ differential function is singular into another linear hybrid system whose coefficient matrix is invertible and doesn’t change the observability of the original system. We then discuss the rank conditions guaranteeing the linear hybrid system observable and give some examples. Finally we present the conclusions and future work.