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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.

This paper aims to focus on the design of a decentralized observation and control method for a class of large-scale systems characterized by nonlinear interconnected functions that are assumed to be uncertain but quadratically bounded.

Sufficient conditions, under which the designed control scheme can achieve the asymptotic stabilization of the augmented system, are developed within the Lyapunov theory in the framework of linear matrix inequalities (LMIs).

The derived LMIs are formulated under the form of an optimization problem whose resolution allows the concurrent computation of the decentralized control and observation gains and the maximization of the nonlinearity coverage tolerated by the system without becoming unstable. The reliable performances of the designed control scheme, compared to a distinguished decentralized guaranteed cost control strategy issued from the literature, are demonstrated by numerical simulations on an extensive application of a three-generator infinite bus power system.

The developed optimization problem subject to LMI constraints is efficiently solved by a one-step procedure to analyze the asymptotic stability and to synthesize all the control and observation parameters. Therefore, such a procedure enables to cope with the conservatism and suboptimal solutions procreated by optimization problems based on iterative algorithms with multi-step procedures usually used in the problem of dynamic output feedback decentralized control of nonlinear interconnected systems.

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 purpose of this paper is to concern the design of a robust model predictive controller for distributed networked systems with transmission delays.

The overall system is composed of a number of interconnected nonlinear subsystems with time-varying transmission delays. A distributed networked system with transmission delays is modeled as a nonlinear system with a time-varying delay. Time delays appear in distributed systems due to the information transmission in the communication network or transport of material between the sub-plants. In real applications, the states may not be available directly and it could be a challenge to address the control problem in interconnected systems using a centralized architecture because of the constraints on the computational capabilities and the communication bandwidth. The controller design is characterized as an optimization problem of a “worst-case” objective function over an infinite moving horizon.

The aim is to propose control synthesis approach that depends on nonlinearity and time varying delay characteristics. The MPC problem is represented in a time varying delayed state feedback structure. Then the synthesis sufficient condition is provided in the form of a linear matrix inequality (LMI) optimization and is solved online at each time instant. In the rest, an LMI-based decentralized observer-based robust model predictive control strategy is proposed.

The authors develop RMPC strategies for a class of distributed networked systems with transmission delays using LMI-Based technique. To evaluate the applicability of the developed approach, the control design of a networked chemical reactor plant with two sub-plants is studied. The simulation results show the effectiveness of the proposed method.

The purpose of this paper is to analyze the load balancing (LB) problem in clusters of heterogeneous processors using delayed artificial neural networks theory, optimal control theory, and linear matrix inequalities (LMIs).

Starting with a mathematical model that includes delays and processors with different processing velocities, this model is transformed into a special case of a neural network model known as delayed cellular neural network (DCNN) model. A new energy function is proposed to this delayed neural network special case, assuring convergence conditions through the use of LMIs. Some performance criteria subject to stability conditions to the non‐linear model version are analyzed, and a new LB controller systematic method of synthesis is proposed, using two coupled LMIs – one guaranteeing global convergence and the other guaranteeing performance in a linear region of operation. Simulations and experiments proves the efficiency of this approach, reducing LB time with a viable computational cost for clusters with high number of processors.

A new approach for the LB problem was proposed based on an special case of a delayed neural network model. Performance criterium can also be imposed over it using a quadratic cost function, giving a possibility to extend the idea to other classes of delayed neural network.

The novelty associated with this paper is the introduction of an approach which the LB problem on an heterogeneous cluster of local processors can be modeled as a delayed neural network and the performance of the LB algorithm can be imposed, at least locally, by a quadratic cost function. Also, the delayed neural network can also be seen as a Persidskii system with delay.

The purpose of this paper is to present the methodology to the robust stability analysis of a vision‐based control loop in an uncalibrated environment. The type of uncertainties considered is the parametric uncertainties. The approach adopted in this paper utilizes quadratic Lyapunov function to determine the composite Jacobian matrix and ensures the robust stability using linear matrix inequality (LMI) optimization. The effectiveness of the proposed approach can be witnessed by applying it to two‐link robotic manipulator with the camera mounted on the end‐effector.

The objective of this research is the analysis of uncertain nonlinear system by representing it in differential‐algebraic form. By invoking the suitable system representation and Lyapunov analysis, the stability conditions are described in terms of linear matrix inequalities.

The proposed method is proved robust in the presence of parametric uncertainties.

Through a differential‐algebraic equation, LMI conditions are devised that ensure the stability of the uncertain system while providing an estimate of the domain of attraction based upon quadratic Lyapunov function.

The purpose of this paper is to propose a stability analysis and control synthesis for achieving passivity properties of a class of continuous‐time nonlinear systems. These nonlinear systems are represented via continuous affine Takagi‐Sugeno (T‐S) fuzzy models, which played an important role in nonlinear control systems. The affine T‐S fuzzy models are more approximate than homogeneous T‐S fuzzy models for modeling nonlinear systems. Using the energy concept of passivity theory with Lyapunov function, the conditions are derived to ensure the passivity and stability of nonlinear systems. Based on the parallel distribution compensation (PDC) technique, this paper proposes a fuzzy controller design approach to achieve the passivity and stability for the continuous affine T‐S fuzzy systems.

For solving stability and stabilization problems of affine T‐S fuzzy models, the conversion techniques and passive theory are employed to derive the stability conditions. By applying the linear matrix inequality technique, a modified iterative linear matrix inequality algorithm is proposed to determine and update the auxiliary variables for finding feasible solutions of these stability conditions.

By studying the numerical example, the proposed design technique of this paper is an effectiveness and useful approach to design the PDC‐based fuzzy controller. From the simulation results, the considered nonlinear system with external disturbances driven by proposed design fuzzy controller is stable and strictly input passive.

This paper is interesting for designing fuzzy controller to guarantee the stability and strict input passivity of affine T‐S fuzzy models.

The purpose of this paper is to stabilize the type-2 Takagi–Sugeno (T–S) fuzzy systems with the sufficient and guaranteed stability conditions. The given conditions efficaciously handle parameter uncertainties by the upper and lower membership functions of the type-2 fuzzy sets (FSs).

This paper reports on a relevant study of stable fuzzy controllers and type-2 T–S fuzzy systems and reported that the synthesis of controller for nonlinear systems described by the type-2 T–S fuzzy model is a key problem and it can be resolve to convex problems via linear matrix inequalities (LMIs).

The multigain fuzzy controllers are established to improve the solvability of the stability conditions, and the authors design multigain fuzzy controllers which have extensive information of upper and lower membership grades. Consequently, the authors derive the traditional stability condition in terms of LMIs. One simulation examples illustrate the effectiveness and robustness of the derived stabilization conditions.

The uncertain MIMO nonlinear system described by Type-2 Takagi-Sugeno (T-S) fuzzy model, and successively LMI approach used to determine the system stability conditions. The proposed control approach will give superior fault-tolerant control permanence under the actuator fault [partial loss of effectiveness (LOE)]. Also the controller robust against the unmeasurable process disturbances. Additionally, the statistical z-test are carried out to validate the proposed control approach against the control approach proposed by Himanshukumar and Vipul (2019a).

In this chapter, we discuss initiatives that aim to improve children’s literacy in low- and middle-income (LMI) countries through m-learning. These projects, predominantly introduced by governments and international aid organisations, often involve the provision of e-books and apps including game-based apps, to be used either inside or outside school. In some cases, lesson plans and content for teachers in poorly resourced schools are also delivered via mobile devices. After a general overview, we briefly describe a selection of projects with reference to m-learning and literacy theory and research. It is indicated in this chapter that the use of mobile devices to improve literacy opportunities for children in LMI countries has a great deal of potential but that, in many cases, there are limitations in pedagogical design and implementation practices, not to mention restricted views of what literacy is and might be for children in these locations.

The purpose of this paper is to propose a guaranteed cost control design procedure for model-based cyber–physical assembly (CPA) systems. To reflect the cyber–physical environment, the network-induced delays and disturbances are introduced in the mathematical model.

Based on the linear matrix inequality approach, the guaranteed cost controller is designed such that the guaranteed cost can be satisfied and the corresponding convex optimization algorithm is provided. Moreover, H-infinity theory is used to deal with the disturbance with the given H-infinity attenuation level.

By constructing appropriate Lyapunov–Krasovskii functionals, delay-dependent sufficient conditions are established in terms of linear matrix inequalities and the controller design procedure is given.

A simplified CPA model is given based on which the designed controller can allow us to control the closed-loop CPA systems with the guaranteed cost.