Determinability and state estimation for switched differential-algebraic equations

TL;DR

This paper addresses the challenge of state estimation for switched differential-algebraic systems by introducing a new observability concept and proposing estimators that guarantee asymptotic convergence.

Contribution

It introduces a novel observability notion for switched DAE systems and develops estimators ensuring asymptotic state convergence.

Findings

Derived an explicit state reconstruction formula.

Proposed estimators with guaranteed asymptotic convergence.

Enhanced understanding of observability in switched DAE systems.

Abstract

The problem of state reconstruction and estimation is considered for a class of switched dynamical systems whose subsystems are modeled using linear differential-algebraic equations (DAEs). Since this system class imposes time-varying dynamic and static (in the form of algebraic constraints) relations on the evolution of state trajectories, an appropriate notion of observability is presented which accommodates these phenomena. Based on this notion, we first derive a formula for the reconstruction of the state of the system where we explicitly obtain an injective mapping from the output to the state. In practice, such a mapping may be difficult to realize numerically and hence a class of estimators is proposed which ensures that the state estimate converges asymptotically to the real state of the system.