Pre‐filtering and post‐filtering in gain‐scheduled output‐feedback control

Linear matrix inequality (LMI) design conditions for gain‐scheduled output‐feedback control rely on assumptions constraining either system or controller matrices. Throughout the literature, it is common practice to avoid imposing restrictive assumptions on the controller, which may appear undesirable, in favor of state augmentations via pre‐filtering and post‐filtering to construct auxiliary augmented systems that comply with the alternative assumptions on the system matrices. This technique brings in the additional cost of increased state dimensions of the resulting gain‐scheduled output‐feedback controllers. In this paper, we explore the interplay and inherent trade‐offs between state augmentation, controller structure, and performance. We revisit LMI design conditions for quadratic output‐feedback control and demonstrate that state augmentation via pre‐filtering and post‐filtering in order to avoid constraints on the controller matrices is never advantageous even without taking into account the added complexity and propensity for numerical issues associated with state augmentation. As an additional contribution, we extend this observation to recently introduced modified LMI conditions allowing combined – however less restrictive – assumptions on system and controller matrices. Copyright © 2016 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.     

Robust passivity based resilient control for networked control systems with random gain fluctuations

The problem of resilient controller design for a class of networked control system based on passivity theory is presented. By using the Lyapunov–Krasovskii stability theory and linear matrix inequality approach, a set of sufficient conditions for the existence of state feedback controllers is derived. The networked control system under consideration is modeled by taking the network‐induced imperfections like packet dropouts and transmission delays as a single time‐varying delay. The controller is considered with a stochastic fluctuations in its gain matrix by using the Bernoulli distributed white sequence with time‐varying probability measures. The probability‐dependent sufficient conditions are established to guarantee the resulting closed‐loop system to be stochastically stable with a prescribed mixed and passivity performance criterion. The results are expressed in the form of convex optimization problem subject to the set of LMIs, which can be easily solved by using some standard numerical packages. Finally, a numerical example by using the high‐incidence research model is presented to illustrate the effectiveness and applicability of the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Iterative ‐conic controller synthesis

This paper proposes a method to synthesize controllers that minimize an upper bound on the closed‐loop ‐norm while imposing desired controller conic bounds. An initial conic controller is synthesized and iteratively improved. Conic sectors can be used to characterize a variety of input‐output properties, such as gain, phase, and minimum gain. If such plant properties hold robustly to uncertainty present, then closed‐loop stability can be ensured robustly via the Conic Sector Theorem by imposing desired controller conic bounds. Consequently, this paper provides a versatile optimal and robust controller synthesis method. Moreover, it relies only on the solution of convex optimization problems subject to linear matrix inequality constraints, making it readily implementable.     

Stabilization of stochastic coupled systems with Markovian switching via feedback control based on discrete‐time state observations

This study investigates the stabilization issue of stochastic coupled systems with Markovian switching via feedback control. A state feedback controller based on the discrete‐time observations is applied for the stabilization purpose. By making use of the graph theory and the Lyapunov method, we establish both Lyapunov‐ and coefficient‐type sufficient criteria to guarantee the stabilization in the sense of stability, and then, we further develop the mean‐square asymptotical stability. In particular, the upper bound of the duration between 2 consecutive state observations is well formulated. Applications to a concrete stabilization problem of stochastic coupled oscillators with Markovian switching and some numerical analyses are presented to illustrate and to demonstrate the easy verifiability, effectivity, and efficiency of our theoretical findings.     

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.     

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.     

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.     

Reciprocal convex approach to output‐feedback control of uncertain LPV systems with fast‐varying input delay

Robust control of parameter‐dependent input delay linear parameter‐varying (LPV) systems via gain‐scheduled dynamic output‐feedback control is considered in this paper. The controller is designed to provide disturbance rejection in the context of the induced ‐norm or the norm of the closed‐loop system in the presence of uncertainty and disturbances. A reciprocally convex approach is employed to bound the Lyapunov‐Krasovskii functional derivative and extract sufficient conditions for the controller characterization in terms of linear matrix inequalities (LMIs). The approach does not require the rate of the delay to be bounded, hence encompasses a broader family of input‐delay LPV systems with fast‐varying delays. The method is then applied to the air‐fuel ratio (AFR) control in spark ignition (SI) engines where the delay and the plant parameters are functions of the engine speed and mass air flow. The objectives are to track the commanded AFR signal and to optimize the performance of the three‐way catalytic converter (TWC) through the precise AFR control and oxygen level regulation, resulting in improved fuel efficiency and reduced emissions. The designed AFR controller seeks to provide canister purge disturbance rejection over the full operating envelope of the SI engine in the presence of uncertainties. Closed‐loop simulation results are presented to validate the controller performance and robustness while meeting AFR tracking and disturbance rejection requirements.     

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.     

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.     

A mixed numerical–analytical stable pseudo‐inversion method aimed at attaining an almost exact tracking

This paper considers the problem of computing the input u(t) of an internally asymptotically stable, possibly non‐minimum phase, linear, continuous time system Σ yielding a very accurate tracking of a pre‐specified desired output trajectory . The main purpose of the new approach proposed here is to alleviate some limitations that inherent the classical methods developed in the framework of the preview‐based stable inversion, which represents an important reference context for this class of control problems. In particular, the new method allows one to deal with arbitrary and possibly uncertain initial conditions and does not require a pre‐actuation. The desired output to be exactly tracked in steady state is here assumed to belong to the set of polynomials, exponential, and sinusoidal time functions. The desired transient response is specified to obtain a fast and smooth transition toward the steady‐state trajectory , without under and/or overshoot in the case of a set point reset. The transient control input u_t(t) is a priori assumed to be given by a piecewise polynomial function. Once has been specified, this allows the computation of the unknown u_t(t) as the approximate least squares solution of the Fredholm's integral equation corresponding to the explicit formula of the output forced response. The steady‐state input u_s(t) is analytically computed exploiting the steady‐state output response expressions for inputs belonging to the same set of . Copyright © 2013 John Wiley & Sons, Ltd.     

A less conservative approach to handle time‐varying parameters in discrete‐time linear parameter‐varying systems with applications in networked control systems

This article proposes a new strategy to deal with linear parameter‐varying discrete‐time systems, whose time‐varying parameters can be written as solutions (such as exponential, trigonometric, or periodic function) of a linear difference equation (DE). The novelty is to explicitly exploit the precise knowledge of the function describing the time‐varying parameter by incorporating the associated DE in the conditions, providing less conservative results when compared with conventional approaches based on bounded or arbitrary rates of variation. The advantage of the method comes from the fact that, differently from the available methods, the pointwise stability for the whole domain of the time‐varying parameters is not a necessary condition to obtain feasible solutions. The applicability and benefits of the proposed technique are investigated in terms of numerical examples concerning robust stability analysis,  filtering, and  state‐feedback control. As a final contribution, the problem of time‐varying sampling periods in the context of networked control systems is investigated using the proposed strategy. A numerical example based on a practical application is presented to illustrate the superiority of the approach when compared to methods from the literature based on matrix exponential computation.     

Semiglobal finite‐time synchronization of complex networks with stochastic disturbance via intermittent control

This paper focuses on the problem of semiglobal finite‐time synchronization of stochastic complex networks via an intermittent control strategy. By establishing a finite‐time criterion condition and a novel finite‐time ‐operator differential inequality, combined with convex techniques, some sufficient conditions are obtained to ensure finite‐time synchronization for stochastic complex networks with time delays. An effective controller is given to guarantee inner finite‐time synchronization, especially for a nondelayed dynamic system. This paper provides a simple controller. Finally, a numerical simulation is given to demonstrate the effectiveness of our results.     

Reliable mixed passive and filtering for semi‐Markov jump systems with randomly occurring uncertainties and sensor failures

This paper investigates the reliable mixed passive and filtering problem for uncertain semi‐Markov jump delayed systems subject to sensor failures. The parameter uncertainties are randomly occurring with two stochastic variables, which are mutually independent and satisfy certain probabilistic distributions on the interval [0,1]. The objective is to focus on the design of a reliable filter ensuring the mixed passivity and performance level of the resulting filtering error system in the presence of sensor failures. By using an improved reciprocally convex approach combined with a novel integral inequality, sufficient conditions of mixed passivity and performance analysis for the considered systems are derived. Based on these, a desired reliable filter design method is developed, and the parameters of the filter are readily calculated by employing a simple expression of the desired filter. Three numerical examples are presented to demonstrate the effectiveness and the reduced conservatism of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.