Strong Absolute Stability of Lur’e Descriptor Systems with Impulsive Models in the Linear Subsystem

Descriptor systems which are also referred to as singular systems are described by differential equations and algebraic equations [1]. It has been widely applied in the areas of power systems, economic systems, biological systems, constrained robots, electronic networking, aerospace, chemical process and astronomy (solar activity)[1-4]. Stability of descriptor systems is a basic and important problem in control theory. Stability of linear descriptor systems has been investigated widely. In [5], necessary and sufficient conditions for robust stability of descriptor interval systems are obtained by using structured singular value theory. [6] studies robust stability of impulsive-free uncertain descriptor systems. [7] is concerned with the problem of robust stability for both continuous and discrete singular delay systems, delay-dependent robust stability criteria in terms of strict linear matrix inequality (LMI) are derived. However, the research on nonlinear descriptor systems is premature because of their complex characteristics. In [8], stability problems of a composite descriptor large-scale system are studied by the generalized vector Lyapunov functions. In [9-11], under the assumption that the initial compatible conditions are known, sufficient conditions for stability of the nonlinear descriptor systems are given. [12] is concerned with the quadratic stabilization for a class of switched nonlinear singular systems. [13] gives a sufficient condition for the local stability of nonlinear descriptor systems. [14] studies the solvability and stability of a class of nonlinear descriptor systems. [15] and [16] studies the stability of Lipschitz nonlinear descriptor systems, and sufficient conditions for stability of the systems are given. Lur’e descriptor system (LDS) is a typical nonlinear descriptor system, which is a feedback system whose feed-forward is linear time-invariant system and feedback