Discrete‐time sector based hands‐off control for nonlinear system

This article presents a hands‐off control design for discrete‐time nonlinear system with a special type of nonlinear sector termed as “discrete‐time sector.” The design method to define the boundary of a discrete‐time sector is done with control‐Lyapunov function. The generalization of nonlinear system is viewed in the perspective of a comparison function. By means of a proposed sector, a switching control is designed such that no control action is experienced inside the sector thus, saving unnecessary control efforts. However, to study the robustness for discrete‐time system, a hands‐off control is modified to ensure the monotonic decrease in the energy of the system. Finally, the proposed approach is verified with the simulation results.     

Robust nonfragile observer‐based control of switched discrete singular systems with time‐varying delays: A sliding mode control design

This paper is devoted to the robust sliding mode control issue for a type of switched discrete singular systems with time‐varying delays under arbitrary switching. Since the system states are not available, the nonfragile observer strategy is used to generate the state estimation. By designing a novel sliding surface function, which is established on the estimation, new sufficient conditions via linear matrix inequalities are derived so that the closed‐loop system is admissible with an disturbance attenuation level γ. Furthermore, sliding mode controllers are given to guarantee the reachability of the quasi‐sliding mode and weaken the chattering. At last, examples are presented to verify the validity of our provided approach.     

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.     

Pth moment regional stability/stabilization and generalized pole assignment of linear stochastic systems: Based on the generalized ‐representation method

This paper investigates pth moment regional stability, stabilization, and generalized pole assignment of stochastic systems, which are most useful in many specific systems and applications. With the help of the generalized ‐representation method, the necessary and sufficient conditions of pth moment regional stability and stabilization of stochastic systems are addressed. Meanwhile, the generalized pole assignment of stochastic systems is also considered. Finally, two examples are presented to show the effectiveness of the proposed methods.     

On the dual linear periodic time‐delay system: Spectrum and Lyapunov matrices,with application to analysis and balancing

We present novel theoretical concepts for linear time‐periodic systems with multiple delays, which are closely related to the spectral properties and Lyapunov matrices. At the basis of the main results is the associated dual system, constructed by transposition of the systems matrices and affine transformations of their arguments. We introduce, for the first time, the concepts of the norm and the dual Lyapunov matrix of periodic systems with delays. We show that the primal and dual system have the same norm, characterized by primal and dual delay Lyapunov equations, which extend the well‐known results for time‐invariant systems with delays, and periodic systems without delays. Having at hand the pair of primal‐dual Lyapunov matrices, along with some energy interpretations, allow us to generalize the concept of position balancing and explore its potential for model reduction. The obtained results are illustrated by several examples, including the delayed Mathieu equation.     

Network‐based robust event‐triggered control for continuous‐time uncertain semi‐Markov jump systems

This article investigates the event‐triggered (ET) states feedback robust control problem for a class of continuous‐time networked semi‐Markov jump systems (S‐MJSs). An ET scheme, which depends on semi‐Markov process, is presented to design a suitable controller and save communication resources. To cope with the network transmission delay phenomenon, a time‐delay S‐MJSs model under the ET scheme is introduced to describe this phenomenon. Then, it is assumed that the communication links between event detector and zero‐order holder are imperfect, where the signal quantization and the actuator fault occur simultaneously. The sufficient conditions are derived by means of linear matrix inequalities approach, which guarantees the stochastic stability of the constructed time‐delay S‐MJSs in an optimized performance level. Based on these criteria, the parameters of controller under the ET scheme are readily calculated. Some simulation results with respect to F‐404 aircraft engine system for two kinds of ET parameters are given to validate the proposed method.     

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.     

Observer-based consensus control for multi-agent systems with measurement noises and external disturbances

This study presents a distributed observer-based consensus control for general linear multi-agent systems under measurement noises and external disturbances. By using the state linear transformation with the matrix constructed from the incidence matrix of a virtual chained directed spanning tree, we transform the observer-based consensus problem into an asymptotic stability problem of a corresponding augmented linear system. The augmented linear system consists of the reduced-order system deduced from dynamic equations of the agents and state estimation error system. Based on asymptotic stability of the augmented linear system, we present some sufficient conditions in terms of linear matrix inequalities for the existence of the distributed observer-based consensus controller. Finally, the effectiveness of the proposed approach is illustrated by a numerical example.     

Dynamic event‐triggered control for linear time‐invariant systems with ‐gain performance

In this paper, a novel dynamic event‐triggered control scheme is presented for linear time‐invariant systems. Under this control scheme, criteria that guarantee the asymptotic stability and the ‐stability are derived, by which the triggered parameters and the feedback gain can be codesigned. The stability criteria are derived by using Lyapunov‐based analysis tools, and a new Lyapunov‐Krasovskii functional is constructed to further reduce conservatism. Moreover, the projection technique and the mathematical induction are introduced in the stability analysis. Compared with the existing results for static strategies, the proposed dynamic strategy is more flexible and generates fewer events. Finally, simulation examples are provided to demonstrate the effectiveness of this new scheme.     

Stubborn state estimation for nonlinear distributed parameter systems subject to measurement outliers

In this article, the state estimation problem is investigated for a class of distributed parameter systems (DPSs). In order to estimate the state of DPSs, we give a partition of spatial interval with a finite sequence and, on each subinterval, one sensor is placed to receive the measurements from the DPS. Due to the unexpected environment changes, the measurements will probably contain some outliers. To eliminate the effects of the possibly occurring outliers, we construct a stubborn state estimator where the innovation is constrained by a saturation function. By using Lyapunov functional, Wirtinger inequality and piecewise integration, some sufficient conditions are obtained under which the resulting estimation error system is exponentially stable and the performance requirement is satisfied. According to the obtained analysis results, the desired state estimator is designed in terms of the solution to a set of matrix inequalities. Finally, a numerical simulation example is given to verify the effectiveness of the proposed state estimation scheme.     

Computation of lower bounds for the induced norm of LPV systems

Determining the induced norm of a linear parameter‐varying (LPV) system is an integral part of many analysis and robust control design procedures. Most prior work has focused on efficiently computing upper bounds for the induced norm. The conditions for upper bounds are typically based on scaled small‐gain theorems with dynamic multipliers or dissipation inequalities with parameter‐dependent Lyapunov functions. This paper presents a complementary algorithm to compute lower bounds for the induced norm. The proposed approach computes a lower bound on the gain by restricting the parameter trajectory to be a periodic signal. This restriction enables the use of recent results for exact calculation of the norm for a periodic linear time varying system. The proposed lower bound algorithm also returns a worst‐case parameter trajectory for the LPV system that can be further analyzed to provide insight into the system performance. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust control of systems with sector nonlinearities via convex optimization: A data‐driven approach

In this paper, a new data‐driven method for designing robust controllers is proposed for systems with sector‐bounded nonlinearities and multimodel uncertainties. The results from the circle criterion are used to generate necessary and sufficient convex constraints that guarantee the stability of the closed‐loop system. The main feature of the proposed approach is that only the frequency response data of the linear part of the system is used for guaranteeing the stability of the closed‐loop nonlinear system. Additionally, a convex optimization problem is formulated to ensure performance with respect to the fundamental component of a sector‐bounded nonlinearity. The case study illustrates how the proposed method can be used to control uncertain systems that are subject to sector‐bounded nonlinearities.     

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.     

Hidden Markov model based filtering for singular semi-Markov jump systems

This article investigates the hidden Markov model based filter design problem for the singular semi-Markov jump systems (SSMJSs). The considered semi-Markov process is a generalization of Markov process, which can eliminate the restriction on the exponential distribution of sojourn time. Besides, the hidden Markov model based filter is introduced to tackle the asynchronous phenomenons occurred between the system modes and filter modes. To ensure the stochastic stability of the SSMJSs and derive solvable filter parameters, a filter design technic is constructed. First, the direct evolution of the states between two arbitrary close time instants is constructed from the filtering error system according to slow-fast decomposition, sufficient conditions are then proposed based on the consistent projector of the filtering error system and the constructed direct state evolution. Second, a new linear decoupling strategy is presented to deal with the coupled terms under the established stability conditions, which further derives the desired hidden Markov model based filter parameters. A numerical example is given to illustrate the effectiveness of the proposed method.     

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.     

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.     

A new -gain analysis framework for discrete-time switched systems based on predictive Lyapunov function

The work proposes the pre--gain analysis framework based on the newly raised nonweighted pre--gain performance index and predictive Lyapunov function, which is devoted to nonweighted -gain analysis and relevant control of discrete-time switched systems under mode-dependent average dwell time. This also provides new ideas for other disturbance-related studies. To begin with, the predictive Lyapunov function is established for switched nonlinear systems in the sense of better reflecting future system dynamics and future external disturbances. Hence, it is achievable to develop less conservative stability and nonweighted pre--gain criteria for switched linear systems. Further, a new disturbance-output expression is devised to match with the nonweighted pre--gain, whose function is to estimate and optimize the traditional nonweighted -gain of the underlying system through discussions. Then, a solvable condition is formulated to seek the piecewise time-dependent gains of switching controller in a convex structure, ensuring the global uniform exponential stability with nonweighted pre--gain and thereby attaining much smaller non-weighted -gain. Finally, the simulation comprised of a circuit system and a numerical example manifests the impressive potential of the obtained results for the purpose of preferable disturbance attenuation performances.     

Direct synthesis of reduced order H controllers for a class of multivariable plants

Given an nth order, -control input, p-measured output generalized plant, this article proposes a simple, direct approach to design an output feedback H controller with order satisfying for , or for . For this purpose, the output feedback H control problem is transformed into an H state feedback problem for an augmented generalized system. A class of plants for which this transformation always exists and the ensuing controller has order as above, is identified. As a result, for such plants, the reduced order H controller gains are found just by solving a simple linear matrix inequality problem used in state feedback based H control. The efficacy of the proposed approach is studied on some benchmark examples.     

Asynchronous control for two‐dimensional hidden Markovian jump systems with partly known mode observation conditional probabilities

This study focuses on the asynchronous control problem for two‐dimensional discrete‐time hidden Markovian jump systems where the mode observation conditional probability matrix is partly known. Considering the original system modes are invisible, the observed modes emitted from an observer serve as an alternative for stability analysis and controller design where a mode observation conditional probability matrix is constructed to characterize the emission between system modes and observed modes. Specially, only partly known information of the mode observation conditional probability matrix is accessible. With the introduction of the free‐connection weighting matrices, the asymptotic mean square stability criterion is firstly derived based on Lyapunov method. This introduction provides a further degree of relaxation and less conservatism is therefore achieved. Secondly, we present synthesis conditions for asynchronous state feedback controller design given in terms of a set of interconnected linear matrix inequalities. Moreover, cluster concept based on the partitions of observed modes is adopted which helps to decrease the number of controllers and simplify the design complexity. A numerical example, regarding the cases with and without clustering of the observed modes, is presented to illustrate the effectiveness of the proposed method.     

An iterative approach for the discrete‐time dynamic control of Markov jump linear systems with partial information

The , and mixed dynamic output feedback control of Markov jump linear systems in a partial observation context is studied through an iterative approach. By partial information, we mean that neither the state variable x(k) nor the Markov chain θ(k) are available to the controller. Instead, we assume that the controller relies only on an output y(k) and a measured variable coming from a detector that provides the only information of the Markov chain θ(k). To solve the problem, we resort to an iterative method that starts with a state‐feedback controller and solves at each iteration a linear matrix inequality optimization problem. It is shown that this iterative algorithm yields to a nonincreasing sequence of upper bound costs so that it converges to a minimum value. The effectiveness of the iterative procedure is illustrated by means of two examples in which the conservatism between the upper bounds and actual costs is significantly reduced.