We characterize stable differential-algebraic equations (DAEs) using a generalized Lyapunov inequality. The solution of this inequality is then used to rewrite DAEs as dissipative Hamiltonian (dH) on the subspace where solutions evolve. Conversely, we give sufficient conditions guaranteeing stability dH DAEs. Further, for stabilizable descriptor systems construct algebraic Bernoulli which can b...

Switched descriptor systems characterized by a repetitive finite sequence of modes can exhibit state discontinuities at the switching time instants. The amplitudes these depend on consistency projectors modes. A switched ordinary differential equations model whose continuous evolution approximates original system is proposed. Sufficient conditions based linear matrix inequalities ensure that ap...

We consider the problem of strong stabilization of descriptor systems via output feedback. The proposed results are based on the concept of (C, A, E, B)-invariance and its algebraic characterization by coupled Sylvester equations and coupled Lyapunov-like equations. Based either on eigenstructure assignment techniques or on the solution of linear matrix inequalities and equalities, we propose a...

This paper is concerned with synthesis of gain-scheduled controllers by representing LPV systems in the descriptor form. Based on a recent algebraic criterion characterizing dissipativity of descriptor systems, an improved synthesis method is proposed with removing limitations of descriptor representation in existing results. Specifications of exponential decay are also considered. A numerical ...

In this paper, we investigate interpolatory projection framework for model reduction of descriptor systems. With a simple numerical example, we first illustrate that employing subspace conditions from the standard state space settings to descriptor systems generically leads to unbounded H2 or H∞ errors due to the mismatch of the polynomial parts of the full and reducedorder transfer functions. ...

In this paper, we present a new approach to investigate the existence and design of reduced-order proper H∞ controllers that provide the same level of performance as that of full-order controllers. By examining some special features of the LMI-based solvability conditions for the H∞ control problem for descriptor systems, we obtain a refined bound on the order of H∞ controllers, which is indepe...

Descriptor systems present a general mathematical framework for the modelling, simulation and control of complex dynamical systems arising in many areas of mechanical, electrical and chemical engineering. This paper presents a survey of the current theory of descriptor systems, concerning solvability, stability, model reduction, controllability, observability and optimal control.

Different properties of general linear descriptor systems are reviewed (existence of solution, consistency of initial condition, impulse controllability and controllability) and structurally characterized. The invariants are associated to a known feedback canonical form of descriptor systems. The aim is to sort the systems by inclusion properties depending on these characterizations.

Abstract: This paper examines the problem of designing a robust H∞ state-feedback controller for a class of uncertain nonlinear descriptor Markovian jump systems described by a Takagi-Sugeno (TS) fuzzy model with Markovian jumps. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor Markovian jump systems to have an H∞ perform...

We discuss model reduction of linear continuous-time descriptor systems that arise in the control of semidiscretized Stokes equations. Balanced truncation model reduction methods for descriptor systems are presented. These methods are closely related to the proper and improper controllability and observability Gramians and Hankel singular values of descriptor systems. The Gramians can be comput...