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For most practical control system problems, the state variables of a system are not often available or measureable due to technical or economical constraints. In these cases, an observer-based controller design problem, which is involved with using the available information on inputs and outputs to reconstruct the unmeasured states, is desirable, and it has been wide investigated in many practical applications. However, the investigation on a discrete-time singular Markovian jumping system is few so far. This paper aims to consider an observer-based control problem for a discrete-time singular Markovian jumping system and provides a set of easy-used conditions to the proposed control law.

According to the connotation of the separation principle extended from linear systems, a mode-dependent observer and a state-feedback controller is designed and carried out independently via two sets of derived necessary and sufficient conditions in terms of linear matrix inequalities (LMIs).

A set of necessary and sufficient conditions for an admissibility analysis problem related to a discrete-time singular Markovian jumping system is derived to be a doctrinal foundation for the proposed design problems. A mode-dependent observer and a controller for such systems could be designed via two sets of strictly LMI-based synthesis conditions.

The proposed method can be applied to discrete-time singular Markovian jumping systems with transition probability p_ij > 0 rather than the ones with p_ii = 0.

The formulated problem and proposed methods have extensive applications in various fields such as power systems, electrical circuits, robot systems, chemical systems, networked control systems and interconnected large-scale systems. Take robotic networked control systems for example. It is recognized that the variance phenomena derived from network transmission, such as packets dropout, loss and disorder, are suitable for modeling as a system with Markovian jumping modes, while the dynamics of the robot systems can be described by singular systems. In addition, the packets dropout or loss might result in unreliable transmission signals which motivates an observer-based control problem.

Both of the resultant conditions of analysis and synthesis problems for a discrete-time singular Markovian jumping system are necessary and sufficient, and are formed in strict LMIs, which can be used and implemented easily via MATLAB toolbox.

The purpose of this paper is to study the 2D hybrid linear model, which is a method of describing both continuous‐ and discrete‐time dynamics in one system. Singularity of 2D hybrid linear models is a newly occurred problem and a very important question is how to compute the solution of the singular 2D hybrid linear model.

Computation of the solution of mentioned system is based on Laplace transform, Z‐transform and shifting algorithm. The inverse Laplace transform and inverse Z‐transform are used in two cases.

In this paper, a class of 2D singular hybrid linear systems is introduced. Two methods for computation of solutions of the singular hybrid system with nonzero boundary conditions are proposed. Both methods are illustrated by the examples.

Presented methods are a new way for computing the solution of singular 2D hybrid linear systems.

The purpose of this paper is to propose an efficient computational technique, which uses Haar wavelets collocation approach coupled with the Newton-Raphson method and solves the following class of system of Lane–Emden equations:

To deal with singularity, Haar wavelets are used, and to deal with the nonlinear system of equations that arise during computation, the Newton-Raphson method is used. The convergence of these methods is also established and the results are compared with existing techniques.

The authors propose three methods based on uniform Haar wavelets approximation coupled with the Newton-Raphson method. The authors obtain quadratic convergence for the Haar wavelets collocation method. Test problems are solved to validate various computational aspects of the Haar wavelets approach. The authors observe that with only a few spatial divisions the authors can obtain highly accurate solutions for both initial value problems and boundary value problems.

The results presented in this paper do not exist in the literature. The system of nonlinear singular differential equations is not easy to handle as they are singular, as well as nonlinear. To the best of the knowledge, these are the first results for a system of nonlinear singular differential equations, by using the Haar wavelets collocation approach coupled with the Newton-Raphson method. The results developed in this paper can be used to solve problems arising in different branches of science and engineering.

The purpose of this paper is to propose a decentralized observer for large‐scale singular systems.

In this paper, the authors investigate the problem of observers' design for large‐scale singular systems. The proposed decentralized observer is based on a new parameterization of the generalized Sylvester equation solution. The considered system is partitioned into small‐sizes interconnected subsystems with unknown interconnections.

A decentralized observer based on new parameterization of generalized Sylvester equation. The performance of the proposed approach is illustrated by a numerical example.

The proposed approach unites the full‐order, the reduced‐order and the minimal order observer design for large‐scale system. The conditions of the existence of this observer are given in the linear matrix inequalities (LMI) form.

The numerical methods are of great importance for approximating the solutions of a system of nonlinear singular ordinary differential equations. In this paper, the authors present the biorthogonal flatlet multiwavelet collocation method (BFMCM) as a numerical scheme for a class of system of Lane–Emden equations with initial or boundary or four-point boundary conditions.

The approach is involved in combining the biorthogonal flatlet multiwavelet (BFM) with the collocation method. The authors investigate the properties and procedure of the BFMCM for first time on this class of equations. By using the BFM and the collocation points, the method is constructed and it transforms the nonlinear differential equations problem into a system of nonlinear algebraic equations. The unknown coefficients of the assuming solution are determined by solving the obtained system. Additionally, convergence analysis and numerical stability of the suggested method are provided.

According to the attained results, the proposed BFMCM has more accurate results in comparison with results of other methods. The maximum absolute errors are calculated by using the BFMCM for comparison purposes provided.

The key desirable properties of BFMCM are its efficiency, simple applicability and minimizes errors. Therefore, the proposed method can be used to solve nonlinear problems or problems with singular points.

The purpose of this paper is to propose solutions for both discrete‐time and frequency‐domain designs of unbiased H_∞ functional filters for discrete‐time linear systems affected by bounded norm energy disturbances.

The discrete‐time procedure design is based on the unbiasedness of the functional filter using a Sylvester equation; then the problem is expressed in a singular system one and is solved in terms of linear matrix inequalities (LMIs). The frequency procedure design is derived from discrete‐time domain results by defining some useful matrix fraction descriptions and mainly, establishing the useful and equivalent form of the connecting relationship that parameterizes the dynamics behavior between discrete‐time and z‐domain.

The performance of the proposed approach is illustrated with the aid of a practical example. The proposed methods are easily implementable and concern a more general class of systems, as the transformation of the system in a singular one permits to treat the problem of perturbance advanced.

First, the order of this filter is equal to the dimension of the vector to be estimated, which is benefit in case of control purpose (reduction of time calculation comparing to the full order one). Second, all recent works on the functional filtering consider systems which permit to avoid to have advanced perturbation term in the error dynamics; the authors propose here an approach which resolves the H_∞ filtering problem even when the term is present. In addition, it permit to consider more general class of discrete‐time systems. Furthermore, the LMI approaching the discrete‐time case permits to handle with more general problem (H_∞, L₂−H_∞) than the classical Riccati one.

Two hydrodynamic models of a semiconductor device are considered. The first takes into account thermal and collisional effects, while neglecting viscous terms, which are included in the second. A qualitative analysis of stationary one‐dimensional solutions is performed and a numerical comparison is presented.

To design a reduced‐order controller with loosing little accuracy.

Singular perturbation approach by quasi‐steady state approximation and by Matrix block diagonalization technique is used.

It is shown that few errors occur between the uncorrected and corrected solutions for the fast subsystems while a few errors occur between the two kinds of solutions for the slow subsystems. The uncorrected solution is admissible for most dynamics. If not, it is recommended that the corrected solution be used.

Proportional feedback control gain is obtained by Pole placement method, which may produce an unwanted overshoot in the response.

This paper shows that the corrected controller is successfully applied in the aircraft dynamics and control.

The simulation of magnetic fields with geometric discretization schemes using magnetic vector potentials involves the solution of very large discrete consistently singular curl‐curl systems of equations. Geometric and algebraic multigrid schemes for their solution require intergrid transfer operators of restriction and prolongation that achieve the discrete conservation of integral quantities serving as state‐variables of geometric discretization methods. For non‐conservative restriction operations, a consistency error correction operator related to an algebraic filtering is proposed. Numerical results show the effects of the consistency correction for a non‐nested geometric multigrid method.

The numerical simulation of metal forming processes approximated by means of finite element techniques, require large computational effort, which contradicts the need of interactivity for industrial applications. This work analyses the computational efficiency of algorithms combining elastoplasticity with finite deformation and contact mechanics, and in particular, the optimum solution of the linear systems to be solved through the incremental‐iterative schemes associated with non linear implicit analysis. A method based on domain decomposition techniques especially adapted to contact problems is presented, as well as the improved performance obtained in the application to hot rolling simulation, as a consequence of bandwidth reduction and the differentiated treatment of subdomains along the non linear analysis.