Dynamic output‐feedback control for continuous‐time singular Markovian jump systems

This paper considers a dynamic output‐feedback control for continuous‐time singular Markovian jump systems, whereas the existing research studies in literature focused on state‐feedback or static output‐feedback control. While they have only provided the sufficient conditions, this paper successfully obtains the necessary and sufficient condition for the existence of the dynamic output‐feedback control. Furthermore, this condition is expressed with linear matrix inequalities by the so‐called replacement technique. Two numerical examples show the validity of the resulting control.     

Distributed filtering and synchronization of diffusively state‐coupled heterogeneous systems

This paper studies distributed filtering‐based ssynchronization of diffusively state‐coupled heterogeneous systems. For given heterogeneous subsystems and a network topology, sufficient conditions for the filtering‐based synchronization are developed with a guaranteed performance. The estimation and synchronization error dynamics are obtained in a decoupled form, and it is shown that the filter and the controller can be designed separately by LMIs. The feasibility of the proposed design method using LMIs is discussed, and the main results are validated through examples with various setup. Copyright © 2016 John Wiley & Sons, Ltd.     

Mixed control of hidden Markov jump systems

In this work, we study the mixed control for Markov jump linear systems with hidden Markov parameters. The hidden Markov process is denoted by , where the nonobservable component θ(k) represents the mode of operation of the system, whereas represents the observable component provided by a detector. The goal is to obtain design techniques for mixed control problems, with the controllers depending only on the estimate , for problems formulated in 3 different forms: (i) minimizing an upper bound on the norm subject to a given restriction on the norm; (ii) minimizing an upper bound on the norm, while limiting the norm; and (iii) minimizing a weighted combination of upper bounds of both the and norms. We propose also new conditions for synthesizing robust controllers under parametric uncertainty in the detector probabilities and in the transition probabilities. The so‐called cluster case for the mixed control problem is also analyzed under the detector approach. The results are illustrated by means of 2 numerical examples.     

A new approach to constrained state estimation for discrete‐time linear systems with unknown inputs

This paper addresses the problem of estimating the state for a class of uncertain discrete‐time linear systems with constraints by using an optimization‐based approach. The proposed scheme uses the moving horizon estimation philosophy together with the game theoretical approach to the filtering to obtain a robust filter with constraint handling. The used approach is constructive since the proposed moving horizon estimator (MHE) results from an approximation of a type of full information estimator for uncertain discrete‐time linear systems, named in short ‐MHE and –full information estimator, respectively. Sufficient conditions for the stability of the ‐MHE are discussed for a class of uncertain discrete‐time linear systems with constraints. Finally, since the ‐MHE needs the solution of a complex minimax optimization problem at each sampling time, we propose an approximation to relax the optimization problem and hence to obtain a feasible numerical solution of the proposed filter. Simulation results show the effectiveness of the robust filter proposed.     

H∞ model predictive control for constrained discrete‐time piecewise affine systems

This paper investigates stability analysis for piecewise affine (PWA) systems and specifically contributes a new robust model predictive control strategy for PWA systems in the presence of constraints on the states and inputs and with l₂ or norm‐bounded disturbances. The proposed controller is based on piecewise quadratic Lyapunov functions. The problem of minimization of the cost function for model predictive control design is changed to minimization of the worst case of the cost function. Then, this objective is reduced to minimization of a supremum of the cost function subject to a terminal inequality by considering the induced l₂‐norm. Finally, the predictive controller design problem is turned into a linear matrix inequality feasibility exercise with constraints on the input signal and state variables. It is shown that the closed‐loop system is asymptotically stable with guaranteed robust performance. The validity of the proposed method is verified through 3 well‐known examples of PWA systems. Simulation results are provided to show good convergence properties along with capability of the proposed controller to reject disturbances.     

Graphical tuning method of FOPID controllers for fractional order uncertain system achieving robust ‐stability

This paper focuses on the graphical tuning method of fractional order proportional integral derivative (FOPID) controllers for fractional order uncertain system achieving robust ‐stability. Firstly, general result is presented to check the robust ‐stability of the linear fractional order interval polynomial. Then some alternative algorithms and results are proposed to reduce the computational effort of the general result. Secondly, a general graphical tuning method together with some computational efficient algorithms are proposed to determine the complete set of FOPID controllers that provides ‐stability for interval fractional order plant. These methods will combine the results for fractional order parametric robust control with the method of FOPID ‐stabilization for a fixed plant. At last, two important extensions will be given to the proposed graphical tuning methods: determine the ‐stabilizing region for fractional order systems with two kinds of more general and complex uncertainty structures: multi‐linear interval uncertainty and mixed‐type uncertainties. Numerical examples are followed to illustrate the effectiveness of the method. Copyright © 2015 John Wiley & Sons, Ltd.     

and control design for polytopic continuous‐time Markov jump linear systems with uncertain transition rates

This paper investigates the problems of and state feedback control design for continuous‐time Markov jump linear systems. The matrices of each operation mode are supposed to be uncertain, belonging to a polytope, and the transition rate matrix is considered partly known. By appropriately modeling all the uncertain parameters in terms of a multi‐simplex domain, new design conditions are proposed, whose main advantage with respect to the existing ones is to allow the use of polynomially parameter‐dependent Lyapunov matrices to certify the mean square closed‐loop stability. Synthesis conditions are derived in terms of matrix inequalities with a scalar parameter. The conditions, which become LMIs for fixed values of the scalar, can cope with and state feedback control in both mode‐independent and mode‐dependent cases. Using polynomial Lyapunov matrices of larger degrees and performing a search for the scalar parameter, less conservative results in terms of guaranteed costs can be obtained through LMI relaxations. Numerical examples illustrate the advantages of the proposed conditions when compared with other techniques from the literature. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust non‐fragile control for delayed singular Markovian jump systems with actuator saturation and partially unknown transition probabilities

The paper is devoted to the investigation of the problem of robust non‐fragile control for singular Markovian jump systems with time‐varying delay and saturating actuators under partially unknown transition probabilities. By employing a Lyapunow function, a mode‐dependent robust non‐fragile state feedback controller, as well as an estimate of the domain of attraction in the mean square sense, is derived to guarantee stochastic admissibility of the corresponding closed‐loop system with actuator saturation. The controller parameters can be obtained by solving a series of linear matrix inequalities. An illustrative example is provided to show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Design and analysis of wideband U‐slot patch antenna with U‐shaped parasitic elements

A single layer single probe‐fed wideband microstrip antenna is presented and investigated. By cutting a U‐slot in the rectangular patch, and by incorporating two identical U‐shaped parasitic patches around both the radiating edges and the nonradiating edges of the rectangular patch, three resonant frequencies are excited to form the wideband performance. Details of the antenna design is presented. The measured and simulated results are in good agreement, the measured impedance bandwidth is GHz ( GHz), or centered at GHz, which covers WLAN GHz ( GHz), WLAN GHz ( GHz), and WIMAX GHz ( GHz) bands. The measured peak gains at the three resonant frequencies are dB, dB, and dB, respectively. An equivalent circuit model which is based on the transmission line theory, the asymmetric coupled microstrip lines theory, and the π‐network theory is established. This equivalent circuit model is used to give an insight into the wideband mechanism of the proposed antenna, and is also used to explain why the three resonant frequencies shift at the variations of different parameters from a physical point of view. The error analysis is given to demonstrate the validity of the equivalent circuit model.     

Another view on q‐rung orthopair fuzzy sets

In this paper, two new approaches have been presented to view q‐rung orthopair fuzzy sets. In the first approach, these can viewed as L‐fuzzy sets, whereas the second approach is based on the notion of orbits. Uncertainty index is the quantity , which remains constant for all points in an orbit. Certain operators can be defined in q‐ROF sets, which affect when applied to some q‐ROF sets. Operators , , and have been defined. It is studied that how these operators affect when applied to some q‐ROF set A.     

Thin‐slot formalism for the split‐field FDTD analysis of periodic structure

An expression of the thin‐slot formalism is presented to alleviate the gridding of the split‐field finite‐difference time‐domain (FDTD) solution for periodic structure. The varying auxiliary‐field ( , ) and split‐field ( , ) distributions near the slots are analytically derived from the varying field ( , ). The update equations for the split‐field FDTD are obtained by incorporating those varying field distributions into the split‐field equations in integral form. A frequency selective surface (FSS) structure is applied to verify the proposed method. The results indicate that the computational efficiency is improved.     

Reliable exponential filtering for singular Markovian jump systems with time‐varying delays and sensor failures

This paper deals with the problem of exponential filtering for singular Markovian jump systems with time‐varying delays subject to sensor failures. The main objective is to design a reliable filtering such that the considered filtering error system in the presence of a time‐varying delay and sensor failures is mean‐square exponentially admissible with a specified decay rate and simultaneously satisfies an performance. First, the delay interval is partitioned into m subintervals and a novel mode‐dependent stochastic Lyapunov‐Krasovskii functional is constructed. By using the reciprocally convex inequality in each subinterval, sufficient conditions of exponential performance analysis are developed for the considered filtering error system. Then, based on these conditions, the existence conditions of the desired reliable filter are derived and the filter parameters are obtained. It should be mentioned that all the results presented here are not only dependent on the time delay but also dependent on the decay rate and the partitioning size. Furthermore, all the conditions are established in terms of strict linear matrix inequalities. Finally, two numerical examples are given to illustrate the less conservatism and effectiveness of the proposed methods.     

Weighted control with ‐stability constraint for switched positive linear systems

This paper is concerned with the problem of control with ‐stability constraint for a class of switched positive linear systems. The ‐stability means that all the poles of each subsystem of the resultant closed‐loop system belong to a prescribed disk in the complex plane. A sufficient condition is derived for the existence of a set of state‐feedback controllers, which guarantees that the closed‐loop system is not only positive and exponentially stable with each subsystem ‐stable but also has a weighted performance for a class of switching signals with average dwell time greater than a certain positive constant. Both continuous‐time and discrete‐time cases are considered, and all of the obtained conditions are formulated in terms of linear matrix inequalities, whose solution also yields the desired controller gains and the corresponding minimal average dwell time. Numerical examples are given to illustrate the effectiveness of the presented approach.Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive asymptotic stabilization of switched parametric strict‐feedback systems with switched control

This paper is concerned with the problem of adaptive stabilization for a class of switched linear‐parametric nonlinear systems under arbitrary switching. The traditional adaptive backstepping control is successfully extended to switched systems from nonswitched ones where the asymptotic regulation of system state is not destroyed due to rapid or abrupt changes of switching parameters. A new switched adaptive controller is designed by exploiting a common high‐order Lyapunov function with a σ‐modification mechanism, which can reflect sufficiently the changes of plant by designing different adaptive laws and control laws for different subsystems. An explicit formula for constructing a continuous and piecewise virtual control function is given to remove the restriction where some bound functions have to be constructed blindly by designers in the existing results, which may be somewhat too strict to be applied. A numerical example is provided to validate the proposed approach.     

Reliable H ∞ static output control of linear time‐varying delay systems against sensor failures

This paper is concerned with the reliable static output control of linear time‐varying delay systems with sensor faults. Time‐varying delay is tackled by the input–output transformation and the resulting closed‐loop system lies in the framework of scaled small gain. Some techniques are developed to separate the coupling among the Lyapunov matrix, input matrix, control gain matrix, and output matrix. Based on a relaxed Lyapunov–Krasovskii functional, sufficient conditions for the desired static output controller design with the required performance level are proposed by means of linear matrix inequalities. The effectiveness of the proposed method is validated by two examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Constrained estimation for time‐varying networks with hybrid incomplete information

This paper deals with the constrained estimation problem for a class of time‐varying complex networks with hybrid incomplete information including randomly occurring uncertainties, randomly occurring nonlinearities, and fading measurements over a finite horizon. Communication links among nodes have uncertain coupling strengths, which can be transformed into a norm‐bounded inner coupling matrix based on the interval matrix approach. The proposed performance requirements not only quantify the degree of the estimation error with regard to unknown‐but‐bounded disturbances but also confine the estimation error in a constrained set. By exploiting the intensive stochastic analysis and the set‐membership method, sufficient conditions are developed under which networks fulfill the performance and the bounded constraint, respectively. Then, a new criterion is derived to ensure the prescribed requirements in terms of recursive linear matrix inequalities suitable for online computation. Finally, a simulation example is provided to show the effectiveness of the developed results.     

Input‐output triggered control using ‐stability over finite horizons

This paper investigates stability of nonlinear control systems under intermittent information. Following recent results in the literature, we replace the traditional periodic paradigm, where the up‐to‐date information is transmitted and control laws are executed in a periodic fashion, with the event‐triggered paradigm. Building on the small gain theorem, we develop input–output triggered control algorithms yielding stable closed‐loop systems. In other words, based on the currently available (but outdated) measurements of the outputs and external inputs of a plant, a mechanism triggering when to obtain new measurements and update the control inputs is provided. Depending on the noise in the environment, the developed algorithm yields stable, asymptotically stable, and ‐stable (with bias) closed‐loop systems. Control loops are modeled as interconnections of hybrid systems for which novel results on ‐stability are presented. The prediction of a triggering event is achieved by employing ‐gains over a finite horizon. By resorting to convex programming, a method to compute ‐gains over a finite horizon is devised. Finally, our approach is successfully applied to a trajectory tracking problem for unicycles. Copyright © 2014 John Wiley & Sons, Ltd.     

Parameterized LMIs for robust and state feedback control of continuous‐time polytopic systems

This paper presents new extended linear matrix inequality (LMI) characterizations for the synthesis of robust and state feedback controllers for continuous‐time linear time‐invariant systems with polytopic uncertainty. Based on a suitable change of variables and the Elimination Lemma, the proposed robust control design techniques are stated as extended LMI conditions parameterized in terms of 2 scalar parameters. One parameter is shown to belong to a bounded domain, thus limiting the scalar search domain. For the other parameter, a bounded subset is provided from numerical experiments. The benefits of the methodology are illustrated through numerical simulations performed on an uncertain model borrowed from the literature. It is shown that the proposed LMI relaxations can provide less conservative results with fewer scalar searches than some existing methods in the literature.     

Quasi‐Time‐Dependent Controller for Discrete‐Time Switched Linear Systems With Mode‐Dependent Average Dwell‐Time

This paper is concerned with the stability and stabilization problem of a class of discrete‐time switched systems with mode‐dependent average dwell time (MDADT). A novel Lyapunov function, which is both mode‐dependent (MD) and quasi‐time‐dependent (QTD), is established. The new established Lyapunov function is allowed to increase at some certain time instants. A QTD controller is designed such that the system is globally uniformly asymptotically stable (GUAS) and has a guaranteed performance index. The new QTD robust controller designed in this paper is less conservative than the mode independent one which is frequently considered in literatures. Finally, a numerical example and a practical example are provided to illustrate the effectiveness of the developed results.      

Delay‐dependent fault‐tolerant controller for time‐delay systems with randomly occurring uncertainties

This paper addresses the passivity‐based control problem for a class of time‐varying delay systems subject to nonlinear actuator faults and randomly occurring uncertainties via fault‐tolerant controller. More precisely, the uncertainties are described in terms of stochastic variables, which satisfies Bernoulli distribution, and the existence of actuator faults are assumed not only linear but also nonlinear, which is a more general one. The main objective of this paper is to design a state feedback‐reliable controller such that the resulting closed‐loop time‐delay system is stochastically stable under a prescribed mixed and passivity performance level γ>0 in the presence of all admissible uncertainties and actuator faults. Based on Lyapunov stability method and some integral inequality techniques, a new set of sufficient conditions is obtained in terms of linear matrix inequality (LMI) constraints to ensure the asymptotic stability of the considered system. Moreover, the control design parameters can be computed by solving a set of LMI constraints. Finally, two examples including a quarter‐car model are provided to show the efficiency and usefulness of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd.