Dissipativity‐based asynchronous control of discrete‐time Markov jump systems with mixed time delays

This paper addresses the problem of dissipativity‐based asynchronous control for a class of discrete‐time Markov jump systems. A unified framework to design a controller for discrete‐time Markov jump systems with mixed time delays is proposed, which is fairly general and can be reduced to a synchronous controller or a mode‐independent controller. Based on a stochastic Lyapunov function approach, which fully utilizes available information of the system mode and the controller, a sufficient condition is established to ensure the stochastic stability and strictly ( , , ) dissipative performance of the resulting closed‐loop system. Finally, the effectiveness and validity of the proposed method are illustrated with a simulation example.     

Finite‐time asynchronous filtering for discrete‐time Markov jump systems over a lossy network

This paper is concerned with the problem of finite‐time asynchronous filtering for a class of discrete‐time Markov jump systems. The communication links between the system and filter are assumed to be unreliable, which lead to the simultaneous occurrences of packet dropouts, time delays, sensor nonlinearity and nonsynchronous modes. The objective is to design a filter that ensures not only the mean‐square stochastic finite‐time bounded but also a prescribed level of performance for the underlying error system over a lossy network. With the help of the Lyapunov–Krasovskii approach and stochastic analysis theory, sufficient conditions are established for the existence of an admissible filter. By using a novel simple matrix decoupling approach, a desired asynchronous filter can be constructed. Finally, a numerical example is presented and a pulse‐width‐modulation‐driven boost converter model is employed to demonstrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

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.     

Decentralized weighted control for a class of large‐scale systems with multi‐modes

In this paper, the control synthesis problem for a class of large‐scale systems with multi‐modes that are called large‐scale switched systems is addressed. By introducing the concept of decentralized switching signal and the relevant decentralized average dwell time, the asymptotic stability and weighted ?₂ gain performance are investigated. It should be noted that the decentralized switching covers general switching cases for large‐scale switched systems, namely, it admits both time‐dependent switching signal and arbitrary switching signal blended in the decentralized switching. Then, on the basis of the analysis results, the decentralized weighted control scheme including state feedback controller gains and switching signals is studied. Several design algorithms are proposed to meet different controller design problems. Finally, numerical examples are provided to illustrate theoretical findings within this paper. Copyright © 2013 John Wiley & Sons, Ltd.     

A novel three‐dimensional guidance law implementation using only line‐of‐sight azimuths

A novel three‐dimensional guidance law using only line‐of‐sight azimuths based on input‐to‐state stability and robust nonlinear observer is proposed for interception of maneuvering targets. The proposed guidance law does not need any prior information of unknown bounded target maneuvers and uncertainties. Since in practice the line‐of‐sight rate is difficult for a pursuer to measure accurately, a nonlinear robust observer is introduced to estimate it. A three‐dimensional guidance law with bearing only measurement is obtained for interception of maneuvering targets. The presented algorithm is tested using computer simulations against a maneuvering target. Copyright © 2014 John Wiley & Sons, Ltd.     

Coordination control of multiple Euler–Lagrange systems for escorting mission

In this paper, a motion control problem of multi‐agent systems for escorting a target is investigated by employing nonsingular fast terminal sliding mode control and adaptive control associated with kinematic control. The proposed control law is robust to model uncertainty and disturbances, and it guarantees all the agents to scatter around the target evenly and escort it with a fixed distance while avoiding obstacles (or collisions) in p‐dimensional case ( is a positive integer). Finite‐time convergence of the position errors and velocity errors is proved rigorously by a Lyapunov‐based approach and finite‐time control techniques. Simulation results in both two‐dimensional and three‐dimensional space are provided to illustrate the effectiveness and high‐precision performance of the control algorithm compared with the traditional adaptive sliding mode control, showing that all the agents can move into suitable positions on the surface of the sphere in the escort mission, and the formation can be reconfigured automatically when the obstacle (or collision) avoidance task is active. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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.     

Fault estimation for discrete‐time switched nonlinear systems with discrete and distributed delays

This paper is concerned with the fault estimation for a class of discrete‐time switched nonlinear systems with mixed time delays. The fault existing in the system is assumed to be characterized by an external system, which incorporates the fault's prior knowledge to the considered systems. The fault estimator is designed by using the multiple Lyapunov–Krasovskii functional and average dwell‐time approach. Sufficient conditions in the form of linear matrix inequalities (LMIs) are developed to ensure the resulting error system is exponentially stable with an optimized disturbance attenuation level. The gain matrices of the estimator can be easily determined by using the standard optimization toolboxes. Finally, numerical examples and simulation results with the help of real‐time systems are given to illustrate the effectiveness and advantages of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.     

state estimation with fading measurements,randomly varying nonlinearities and probabilistic distributed delays

In this paper, the state estimation problem is investigated for a class of discrete‐time stochastic systems in simultaneous presence of three network‐induced phenomena, namely, fading measurements, randomly varying nonlinearities and probabilistic distributed delays. The channel fading is characterized by the ?th‐order Rice fading model whose coefficients are mutually independent random variables with given probability density functions. Two sequences of random variables obeying the Bernoulli distribution are utilized to govern the randomly varying nonlinearities and probabilistic distributed delays. The purpose of the problem addressed is to design an state estimator such that the dynamics of the estimation errors is stochastically stable and the prespecified disturbance rejection attenuation level is guaranteed. Through intensive stochastic analysis, sufficient conditions are established under which the addressed state estimation problem is recast as a convex optimization one that can be solved via the semi‐definite program method. Finally, a simulation example is provided to show the usefulness of the proposed state estimation scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Discrete‐time output feedback for Markov jump systems with uncertain transition probabilities

This article addresses the output feedback control for discrete‐time Markov jump linear systems. With fully known transition probability, sufficient conditions for an internal model based controller design are obtained. For the case where the transition probabilities are uncertain and belong to a convex polytope with known vertices, we provide a sufficient LMI condition that guarantees the norm of the closed‐loop system is below a prescribed level. That condition can be improved through an iterative procedure. Additionally, we are able to deal with the case of cluster availability of the Markov mode, provided that some system matrices do not vary within a given cluster, an assumption that is suitable to deal with packet dropout models for networked control systems. A numerical example shows the applicability of the design and compares it with previous results. Copyright © 2012 John Wiley & Sons, Ltd.     

A robust observer‐based stabilization method for systems with uncertain parameters and Lipschitz nonlinearities

This paper deals with the robust observer‐based control design for a class of Lipschitz nonlinear discrete‐time systems with parameter uncertainties. Based on the use of a reformulated Lipschitz property combined with the slack variable techniques and some mathematical artifacts, it is shown that the solution of the discrete‐time output feedback stabilization problem is conditioned by a set of bilinear matrix inequalities, which become linear matrix inequalities by freezing some scalars. Furthermore, we show that some existing and elegant results reported in the literature can be regarded as particular cases of the stability conditions presented here. Numerical examples are provided to show the validity and superiority of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.