A Globally Stable Algorithm for the Integration of High-Index Differential-Algebraic Systems

Abstract

The problem of constraint stabilization and numerical integration for differential-algebraic systems is addressed using Lyapunov theory. It is observed that the application of stabilization methods which rely on a linear feedback mechanism to nonlinear systems may result in trajectories with finite escape time. To overcome this problem we propose a method based on a nonlinear stabilization mechanism which guarantees the global existence and convergence of the solutions. Discretization schemes, which preserve the properties of the method, are also presented. The results are illustrated by means of the numerical integration of a slider-crank mechanism.

Actuator Fault Detection for Discrete-Time Descriptor Systems via a Convex Unknown Input Observer with Unknown Scheduling Variables

“…where x k ∈ R n is the state vector, u k ∈ R m is the input vector, and d k ∈ R q is the unknown input vector, y k ∈ R o is the output vector; A(x k ), B(y k ), C(x k ), D(y k ), and E(y k ) are matrix functions whose entries are smooth and bounded in a region Ω x ⊂ R n including the origin. is work only considers the particular case when E(•) is full rank (the case when descriptor matrix is not invertible has been recently treated in [50,51], this case is also referred as differential-algebraicequation (DAE) systems or singular ones [52], and it is out of the scope of this work. Fault diagnosis schemes for this type of systems have been addressed in [53]) for x k ∈ Ω x ; that is, from (1), it is always possible to obtain a standard state-space representation:…”

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

“…In Section 4, it is possible to verify some numerical examples of discrete‐time nonlinear systems modeled in a DAR form. On the other hand, the existence of the inverse in (4) implies that it is considered in this paper difference‐algebraic systems that do not belong to the class of descriptor systems 50‐53 …”

Diseño de Observadores No Lineales para Plantas Mecatrónicas por Medio de LMIs

“…El caso en que la matriz del descriptor no es invertible se ha tratado recientemente en(Di Franco et al, 2020;Arceo et al, 2018), este caso también se conoce como sistemas de ecuación diferencial algebraica (DAE, por sus siglas en inglés) o sistemas singulares(Dai, 1989).…”