Linear Discrete-time Descriptor Systems Research Articles

Robust filtering for uncertain linear discrete-time descriptor systems

This paper is concerned with the problem of robust filtering for uncertain linear discrete-time descriptor systems. The matrices of the system state-space model are uncertain, belonging to a given polytope. A linear matrix inequality based method is proposed for designing a linear stationary filter that guarantees the asymptotic stability of the estimation error and gives an optimized upper bound on the asymptotic error variance, irrespective of the parameter uncertainty. The proposed robust filter design is based on a parameter-dependent Lyapunov function, which is shown to outperform parameter-independent ones.

ROBUST FILTERING FOR UNCERTAIN LINEAR DISCRETE-TIME DESCRIPTOR SYSTEMS

This paper is concerned with the problem of robust filtering for uncertain linear discrete-time descriptor systems. The matrices of the system state-space model are uncertain and supposed to belong to a given polytope. A linear matrix inequality based method is proposed for designing linear stationary strictly proper filters, for the one-step prediction, that guarantee the asymptotic stability of the estimation error and an optimized upper-bound on the asymptotic error variance, irrespective of the parameter uncertainty. The proposed robust filter design is based on a parameter-dependent Lyapunov function.

Regularization of Linear Discrete-Time Periodic Descriptor Systems by Derivative and Proportional State Feedback

In this paper, we consider the regularization problem for the linear time-varying discrete-time periodic descriptor systems by derivative and proportional state feedback controls. Sufficient conditions are given under which derivative and proportional state feedback controls can be constructed so that the periodic closed-loop systems are regular and of index at most one. The construction procedures used to establish the theory are based on orthogonal and elementary matrix transformations and can, therefore, be developed to a numerically efficient algorithm. The problem of finite pole assignment of periodic descriptor systems is also studied.

Some invariants of discrete-time descriptor systems

Many papers analyze the role of controllability and observability indices of normal linear systems in control theory and their use in the study of structural properties. This work introduces these indices for linear discrete-time descriptor systems. Such indices are studied in two different ways, by means of the state-space approach and using its transfer matrix . A canonical form of the state-space system and a special decomposition of the nonproper transfer matrix are considered in order to discuss the reachability and observability indices.

AN LMI APPROACH TOWARDS STABILIZATION OF DISCRETE-TIME DESCRIPTOR SYSTEMS

In this paper descriptor feedback control of high index or even non-regular linear discrete-time descriptor systems is considered. The approach is based on a linear matrix inequality (LMI) characterization (with a Lyapunov-type matrix as matrix variable) of stable and causal descriptor systems. Applying this result to the problem of stabilizing a controlled discrete-time descriptor system by descriptor feedback such that the closed loop is causal, renders a nonlinear matrix inequality with the controller gain matrix and a Lyapunov-type matrix as variables. For the corresponding non-descriptor problem this matrix inequality can be reduced to an LMI by applying Schur's Lemma and a subsequent linearizing change of variables. In the descriptor setup this procedure is not applicable due to the indefiniteness of the occurring Lyapunov-type matrix. Instead, here a two step controller computation is presented, which firstly renders the closed loop system causal. In the second step an LMI based procedure is used to guarantee stability without affecting causality of the closed loop.

Constrained controllability and reachability of linear descriptor systems*

The Paper derives new necessary and sufficient conditons for globally controllability and reachability of linear discrete-time descriptor systems with restrained controls. The main tool of the proofs is based on some extensions of the Banach open mapping theorem to set-valued convex closed functions. Illustrative examples are given.

A note on constrained controllability of linear descriptor systems

In this note, necessary and sufficient conditions are established for global controllability of linear discrete-time descriptor systems with constrained controls