Discrete Descriptor Systems Research Articles

Positive Normalization of Discrete Descriptor System under Disturbance

It is well known the descriptor systems have a wide application field. Usually it appear as a mathematical model of a real problem, mainly the model that involves the input output relationship. It is well known that a descriptor linear system has an unique solution if the pencil matrix of the system is regular. However, there are some systems that are not regular. Moreover, even though the system is regular the solution can contain the noncausal behavior. Therefore, it is necessary to normalize the descriptor system so as it has well behavior. In this paper, we propose a feedback to normalize a discrete descriptor system under disturbance. Furthermore, we establish a sufficient condition in order for the discrete descriptor system under disturbance can be normalized positively.

Ketercapaian dan Keterkontrolan Sistem Deskriptor Diskrit Linier Positif

A positive discrete descriptor system has been widely used in modeling economics, engineering, chemistry and others. In this research, we studied the necessary conditions and sufficient conditions for a positive discrete descriptors system is achieved positive and controlled postively. In addition, it is also studied on sufficient terms and conditions which ensure that discrete systems are null controlled.
 By using linear algebraic method and Inverse Drazin, this research has proved several theorems for discrete descriptors system achieved positive, controlled positively and controlled null. In addition, examples are given as illustrations to reinforce the validity of the proven theorems.

Anisotropy-based suboptimal state-feedback control design using linear matrix inequalities

A computationally efficient method for the design of a suboptimal anisotropic controller for discrete descriptor systems based on convex optimization methods is proposed. Numerical examples are given.

Piecewise observers of rectangular discrete fuzzy descriptor systems with multiple time-varying delays

This paper investigates piecewise observer design for rectangular discrete fuzzy descriptor systems with multiple time-varying delays. Via a series of simple transformations, the considered rectangular descriptor plants are converted into standard ones with multiple time-varying delays. Then, two sufficient delay-dependent conditions for existence of piecewise fuzzy observers are derived based on piecewise Lyapunov functions. Finally, two numerical examples are presented to show the effectiveness of the theoretical results.

Observers of Fuzzy Descriptor Systems with Time-Delays

For discrete fuzzy descriptor systems with time-delays, the problem of designing fuzzy observers is investigated in this paper. Based on an equivalent transformation, discrete fuzzy descriptor systems with time-delays are converted into standard discrete systems with time-delays. Then, via linear matrix inequality (LMI) approach, both delay-dependent and delay-independent conditions for the existence of fuzzy state observers are obtained. Finally, two numerical examples are provided to illustrate the proposed method.

PENYELESAIAN SISTEM DESKRIPTOR LINIER DISKRIT BEBAS WAKTU DENGAN MENGGUNAKAN METODE DEKOMPOSISI KANONIK

The linear discrete descriptor systems are used in many applications, espe-cially in mathematical modeling for biology, economics and electrical engineering. In thispaper, the solving of invariant time linear discrete descriptor systems using the canonicaldecomposition method was studied. The canonical decomposition method reduces thesystems under consideration into two simple subsystems. The solution is obtained fromtwo simple subsystems. An example is given to illustrate this method.

Development of a general robust H ∞ singular filter design method for uncertain discrete descriptor systems with time delay

This paper solves the problem of a delay-dependent general robust H ∞ singular filter design method for uncertain discrete descriptor systems with interval time-varying delay by linear matrix inequality (LMI) technique. Being different from previous approaches, the discrete singular filtering problem with a new Lyapunov function is considered without any changes of variables, Schur complements, and transformations of conditions for robust H ∞ filtering. The purpose is to design a delaydependent general H ∞ filter such that the delayed filtering error descriptor system is regular, causal, and stable with H ∞ norm bound. Moreover, it is shown that the presented design method by the selection of rank in the singular filter provides reduced-order filters including static filter indirectly. Also, the filter design method can be easily extended to uncertain descriptor systems. Finally, numerical examples are presented to illustrate the feasibility and applicability of the proposed method.

Pole placement in non connected regions for descriptor models

Abstract This paper proposes a method to compute a static state feedback control law which achieves a non strict pole assignment on a continuous or a discrete descriptor system. The specification on the closed-loop poles is given in terms of D -stability, i.e. in terms of a pole-clustering region D . In this work, the clustering region is possibly non path-connected since it can result from the union of disjoint and non symmetric subregions. Such a choice, which is original when the design of linear descriptor systems is concerned, is made possible by a technique that enables a partial pole placement via aggregation. The distribution of the finite poles in various subregions can be chosen. Some key steps of the procedure are addressed through strict LMI (Linear Matrix Inequalities). This is an extension of a previous work from conventional to descriptor models. Therefore, not only stability is to be ensured but also, because of infinite poles, regularity and causality or impulse freeness (the whole of those properties being termed admissibility).

Non-fragile controller design for discrete descriptor systems

This paper is concerned with the design problem of non-fragile controller for discrete descriptor systems. The controller gain variations are assumed to be time-invariant and norm-bounded appearing in the controller coefficients. Sufficient conditions for the existence of a static state feedback controller with additive uncertainty and multiplicative uncertainty are obtained in terms of a set of matrix inequalities, respectively. With these conditions, the problems of non-fragile control for discrete descriptor systems are solved. Explicit expressions of desired non-fragile state feedback controllers are also given, and no matrix decomposition is required. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.

Decoupled Wiener state fuser for descriptor systems

By the modem time series analysis method, based on the autoregressive moving average (ARMA) innovation models and white noise estimation theory, using the optimal fusion rule weighted by diagonal matrices, a distributed descriptor Wiener state fuser is presented by weighting the local Wiener state estimators for the linear discrete stochastic descriptor systems with multisensor. It realizes a decoupled fusion estimation for state components. In order to compute the optimal weights, the formulas of computing the cross-covariances among local estimation errors are presented based on cross-covariances among the local innovation processes, input white noise, and measurement white noises. It can handle the fused filtering, smoothing, and prediction problems in a unified framework. Its accuracy is higher than that of each local estimator. A Monte Carlo simulation example shows its effectiveness and correctness.

The robust D-stability analysis of uncertain discrete-delay descriptor systems via genetic algorithms

In this paper, work concerning robust D-stability analysis is considered for discrete descriptor systems with structured uncertainties and multiple time delays. A genetic algorithm is used to make the stability test of the main result more efficient. A delay-dependent robust D-stability criterion is proposed to ensure that all poles of the discrete multiple time-delay descriptor systems subject to uncertainties are located within a disk contained in the unit circle. It will be seen that the system considered in this paper is more general and the proposed robust D-stability criterion is less conservative and easier to check than those presented in recent research. Moreover, a delay-dependent criterion is derived to guarantee that the system is regular, impulse-free, and D-stable. Since the boundary test occurs during the check of the criteria, a genetic algorithm is used to make it more precise. Finally, an example is introduced to illustrate our main results.

Decoupled distributed Kalman fuser for descriptor systems

Linear discrete stochastic descriptor systems with multisensor have been transformed, using the singular value decomposition (SVD), into two reduced-order non-descriptor subsystems with multisensor. Based on the linear minimum variance optimal fusion rule weighted by diagonal matrices, a decoupled distributed Kalman fuser is presented by using the Kalman filtering method and white noise estimation theory. With this procedure it is possible to handle the fused filtering, smoothing, and prediction problems in a unified framework, and realize a decoupled fused estimation for state components. Its accuracy is higher than that of each local Kalman estimator. In order to compute the optimal weights, the formulas of computing the cross-covariances among local estimation errors have been presented. A Monte Carlo simulation example shows its effectiveness.

THE STABILITY CRITERIONS FOR FUZZY DESCRIPTOR SYSTEMS WITH TIME-DELAY

In this paper, we study the stability problem for a kind of Takagi-Sugeno (T-S for short) fuzzy discrete descriptor system with time' delay. We give a main theorem to check the regularity, causality and stability for the system. The theorem gets over the application difficulty of the criterion for the system with large time-delay. And we also show that the regularity and causality for the system without time-delay are equivalent to ones for the system with time-delay. A numerical example is given to demonstrate the effectiveness of method proposed.

THE LINEAR QUADRATIC DYNAMIC GAME FOR DISCRETE-TIME DESCRIPTOR SYSTEMS

The linear quadratic zero-sum dynamic game for discrete time descriptor systems is considered. A method, which involves solving a linear quadratic zero-sum dynamic game for a reduced-order discrete time state space system, is developed to find the linear feedback saddle-point solutions of the problem. Checkable conditions, which are described in terms of two dual algebraic Riccati equations and a Hamiltonian matrix, are given such that the linear quadratic zero-sum dynamic game for the reduced-order discrete time state space system is available. Sufficient conditions for the existence of the solutions are obtained. In contrast with the dynamic game in state space systems, the dynamic game in descriptor systems admits uncountably many linear feedback saddle-point solutions. All these solutions have the same existence conditions and achieve the same value of the dynamic game.

On the Causality of Linear Time Invariant Descriptor Systems

In this paper questions of the following type will be investigated: ‘which general linear time invariant (l.t.i.) time continuous causal or noncausal system can be approximated or represented by (l.t.i.) time discrete descriptor systems?”, and ‘what happens with the causality or acausality of these systems in the approximation process?” Various answers to these questions will be presented as statements of two theorems. These answers strongly depend on the dimension of the state space of the systems considered. Among these the following statements are of primary interest: Finite dimensional (l.t.i.) time continuous descriptor systems are always causal, whereas finite dimensional (l.t.i.) time discrete descriptor systems may be causal or noncausal. On the other hand, infinite dimensional (l.t.i.) time discrete and time continuous descriptor systems may be causal or noncausal. Each general (l.t.i.) system can be approximated by finite dimensional (l.t.i.) time discrete descriptor systems, and represented (exactly) by an infinite dimensional (l.t.i.) time continuous descriptor system.

Linear-Quadratic Optimal Control Problems for Discrete Descriptor Systems

The control in the feedback form and the optimal cost are obtained for four linear-quadratic control problems by discrete descriptor systems in a Hilbert space. Special solutions of the implicit operator Riccati equations used here act in all state space and in general case they are not non-negative definite unlike the operators in the subspace and the non-negative definite solutions, acting in all state space, as it was in other authors papers. The examples show that the considered operator Riccati equations have no non-negative definite solutions though the corresponding optimal control problems have the unique solutions.

Non-Lyapunov stability robustness consideration for discrete linear descriptor systems

Non-Lyapunov stability robustness consideration for discrete linear descriptor systems

A Lyapunov analysis of stability robustness for discrete linear descriptor systems

A Lyapunov analysis of stability robustness for discrete linear descriptor systems

Observer design for discrete nonlinear descriptor systems

A nonlinear observer is considered for a class of discrete nonlinear descriptor systems subject, to unknown inputs and faults. This class is partly characterized by globally Lipschitz nonlinearities, and a member system may be singular and possibly non-causal. The structure proposed for the observer makes it useful for both state estimation for feedback controls and residual generation for fault detection. Results on the existence of solutions are given and some useful bounds are derived which are important in the observer design. The proposed nonlinear observer is based on a transformed system and on the solution of a Riccati equation. The existence, convergence properties and robustness of the observer are investigated by the use of a quadratic Lyapunov function. A design algorithm is given and applied to the estimation of the states of a flexible joint robot.

Realization of noncausal 2-D systems based on a descriptor model

It is shown that a class of linear discrete noncausal two-dimensional systems can be represented by discrete descriptor systems whose coefficients are functions that admit Laurent series expansions on the unit circle in the complex plane. The basic idea is to obtain a conventional state-space realization with coefficient functions for causal and anticausal subsystems in one direction, and then view them as a descriptor system-a single entity. The resulting model is a 1-D descriptor system with coefficient functions defined on the unit circle in the complex plane. Some properties of this model concerning minimality are also investigated. >