H∞ state‐feedback controller design for continuous‐time nonhomogeneous Markov jump systems

This paper studies the problem of H_∞ state‐feedback controller design for continuous‐time nonhomogeneous Markov jump systems. The time‐varying transition rate matrix in continuous‐time domain is considered to lie in a convex bounded domain of polytopic type. By constructing a parameter‐dependent Lyapunov function and fully considering the information about the rate of change of time‐varying parameters, a new sufficient condition on the existence of an H_∞ state‐feedback controller is provided in the form of a parameter‐dependent matrix inequality. Moreover, based on the structure characteristics of Lyapunov matrix and transition matrix, the parameter‐dependent matrix inequality is converted into a finite set of linear matrix inequalities, which can be readily solved. Two numerical examples are provided to demonstrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Observer‐based H∞ control for uncertain singular time‐delay systems with actuator saturation

In this paper, the observer‐based H_∞ control problem for uncertain singular time‐delay systems with actuator saturation is concerned. First, a delay‐dependent linear matrix inequality (LMI) condition is obtained which, guarantees that the uncertain singular time‐delay systems with actuator saturation are regular, impulse free, and asymptotically stable with H_∞ performance condition. Then, with this condition, the estimation of stability region and the design method of observer‐based H_∞ controller are given by solving LMIs and convex optimization problem. Finally, some numerical examples are provided to demonstrate the merit of the obtained results. Copyright © 2015 John Wiley & Sons, Ltd.     

H∞ output tracking control over networked control systems with Markovian jumping parameters

The problem of H_∞ output tracking control over networked control systems (NCSs) with communication limits and environmental disturbances is studied in this paper. A wide range of time‐varying stochastic problem arising in networked tracking control system is reduced to a standard convex optimization problem involving linear matrix inequalities (LMIs). The closed‐loop hybrid NCS is modeled as a Markov jump linear system in which random time delays and packet dropouts are described as two stochastic Markov chains. Gridding approach is introduced to guarantee the finite value of the sequences of transmission delays from sensor to actuator. Sufficient conditions for the stochastic stabilization of the hybrid NCS tracking system are derived by the LMI‐based approach through the computation of the optimal H_∞ performance. The mode‐dependent robust H_∞ output tracking controller is obtained by the optimal iteration method. Numerical examples are given to demonstrate the effectiveness of the proposed robust output tracking controller for NCS. Copyright © 2016 John Wiley & Sons, Ltd.     

A µ‐dependent approach to H∞ control of uncertain switched linear systems with average dwell time

This paper concerns H_∞ control problem for a class of discrete‐time uncertain switched linear systems with average dwell time. The stability result for general discrete‐time switched systems is first explored, and a µ‐dependent approach is then introduced for the considered systems to the H_∞ controller solution. A mode‐dependent state‐feedback controller is designed such that the resulting closed‐loop system is robust exponentially stable and has a prescribed exponential H_∞ performance index. The µ‐dependent existence conditions of desired controller and admissible switching signals are derived and formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the effectiveness of the developed theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.     

H∞ control for sampled‐data linear systems with two Markov processes

This paper is concerned with the design problem of H_∞ digital switching control for linear continuous systems with Markovian jumping parameters. The controller is digital and monitored by the jumping parameters of the plant. The closed‐loop system is a hybrid one defined on a hybrid time space (composed of a continuous‐time and a discrete‐time) and a sample space. The sample space is specified by two separable continuous‐time discrete‐state Markov processes, one appearing in the open‐loop system, and the other appearing in control action, which is different with the traditional Markovian jumping process. Our attention is focused on designing digital output feedback controllers for the system with two Markovian jumping processes such that both stochastic stability and a prescribed H_∞ performance are achieved. The problem of robust H_∞ control for systems with parameters uncertainties is also studied. It is shown that the sampled‐data control problems for linear Markovian jumping systems with and without parameter uncertainties can be solved in terms of the solutions to a set of intercoupled matrix inequalities. Two numerical examples are given to show the design procedures. Copyright © 2005 John Wiley & Sons, Ltd.     

Multiobjective fault‐tolerant fixed‐order/PID control of multivariable discrete‐time linear systems with unmeasured disturbances

In this paper, a multiobjective fault‐tolerant fixed‐order output feedback controller design technique is proposed for multivariable discrete‐time linear systems with unmeasured disturbances. Initially, a multiobjective fixed‐order controller is designed for the system by transforming the problem of tuning the parameters of the controller into a static output feedback problem and solving a mixed H₂/H_∞ optimization problem with bilinear matrix inequalities. Subsequently, the fixed‐order controller is used to construct the closed‐loop system and an active fault‐tolerant control scheme is applied using the input/output data collected from the controlled system. Motivated by its popularity in industry, the proposed method is also used to tune the parameters of proportional‐integral‐derivative controllers as a special case of structured controllers with the fixed order. Two numerical simulations are provided to demonstrate the design procedure and the flexibility of the proposed technique.     

H∞ control of switched linear discrete‐time systems with polytopic uncertainties

In this paper, the problem of designing H_∞ state‐feedback controllers for switched linear discrete‐time systems with polytopic uncertainties is investigated. Two approaches on designing robust and parameter‐dependent H_∞ controllers are proposed and the existence conditions of the desired controllers are derived and formulated in terms of a set of linear matrix inequalities. By solving the corresponding convex optimization problem, the desired controllers are obtained, respectively, and different optimal H_∞ noise‐attenuation level bounds of corresponding closed‐loop systems are given as well. The designed controllers have their own advantages and disadvantages regarding the conservatism and realization complexity. An illustrative example emerging in networked control systems (NCS) and numerical simulations are presented to show the applicability and effectiveness of the obtained theoretic results. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust H∞ control of stochastic time‐delay jumping systems with nonlinear disturbances

This paper deals with the problems of robust stabilization and H_∞ control for a class of uncertain stochastic jumping systems with nonlinear disturbances and time delays. The uncertain parameters are assumed to be norm‐bounded and mode dependent, and the time delays enter into the state matrix, the stochastic perturbation term, as well as the state feedback. The stochastic robust stabilization problem addressed in this paper is to design a state feedback controller with input delay such that, for all admissible uncertainties and the nonlinear disturbances, the closed‐loop system is robustly, stochastically, exponentially stable in the mean square. Moreover, the purpose of the robust H_∞ control problem is to guarantee a specified H_∞ performance index, while still achieving the mean‐square exponential stability requirement for the closed‐loop system. By resorting to the Itô's differential formula and the Lyapunov stability theory, sufficient conditions are derived, respectively, for the robust stabilization and the robust H_∞ control problems. It is shown that the addressed problems can be solved if a set of linear matrix inequalities (LMIs) are feasible. A numerical example is employed to illustrate the usefulness of the proposed LMI‐based design methods. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust reliability method and reliability‐based performance optimization for non‐fragile robust control design of dynamic system with bounded parametric uncertainties

An efficient robust reliability method for non‐fragile robust control design of dynamic system with bounded parametric uncertainties is presented systematically, in which the uncertainties existing in the controlled plant and controller realization are taken into account simultaneously in an integrated framework. Reliability‐based design optimization of non‐fragile robust control for parametric uncertain systems is carried out by optimizing the H₂ and H_∞ performances of the closed‐loop system, with the constraints on robust reliabilities. The non‐fragile robust controller obtained by the presented method may possess a coordinated optimum performance satisfying the precondition that the system is robustly reliable with respect to the uncertainties existing in controlled plant and controller. Moreover, the robustness bounds of uncertain parameters can be provided. The presented formulations are within the framework of linear matrix inequality and thus can be carried out conveniently. It is demonstrated by a numerical example that the presented method is effective and feasible. Copyright © 2016 John Wiley & Sons, Ltd.     

Delay‐dependent robust H ∞ control for uncertain singular time‐delay system with Markovian jumping parameters

The problem of robust H _∞ control for a class of uncertain singular time‐delay systems with Markovian jumping parameters is addressed in this paper. The considered Markovian jump singular systems involve constant time delay and norm‐bounded uncertainties. On the basis of LMI approach, a delay‐dependent condition is proposed, which ensures the nominal Markovian jump singular system to be regular, impulse‐free and stochastically stable. From the delay‐dependent condition, a sufficient condition leading to the existence of a state feedback controller that guarantees the robust admissibility and the H _∞ performance is also given. A numerical example is given to demonstrate the applicability of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust fixed‐order H2 controller for micro air vehicle—design and validation

Design and real‐time validation of a robust fixed‐order H₂ optimal controller for micro aerial vehicle, named Sarika‐2, is presented. Strengthened discrete optimal projection equations, which approximate the first‐order necessary optimality condition, are used for the controller design. Effect of low‐frequency gust disturbance and high‐frequency sensor noise is alleviated through the output sensitivity and control sensitivity minimization. The novelty of this paper is that a single robust H₂ controller, which is designed at the central operating point, ensures simultaneous stabilization of the radio‐controlled aircraft over the entire cruise speed range of 16–26 m/s. The controller is implemented on a digital‐signal‐processor‐based flight computer, and subsequently, it is validated through the real‐time hardware‐in‐loop‐simulation. The responses obtained from the hardware‐in‐loop‐simulation compares well with those obtained from the off‐line simulation. Copyright © 2006 John Wiley & Sons, Ltd.     

Design of simultaneous static output feedback low‐gain H∞ controllers for a collection of time‐delay system

This paper considers the design of simultaneous static output feedback controllers for a finite collection of time‐delay linear systems. By solving a minimization problem, we try to find an output feedback low‐gain controller such that all resultant closed‐loop time‐delay systems are internally stable and satisfy a prespecified H_∞‐norm requirement. Based on the barrier method, necessary conditions for local optimum of the minimization problem are derived. An example is given for illustration.     

Robust H∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

This paper investigates the problem of control design for a class of uncertain switched singular systems with time‐varying delay. Under mode‐dependent average dwell time and using an appropriate Lyapunov‐Krasovskii functional, the exponential admissibility of the system is analyzed. In order to obtain less conservative conditions, the delay partitioning technique is adopted as well as the improved reciprocally convex approach. By means of the developed admissibility condition, a static output feedback controller is then designed using linear matrix inequality approach. Moreover, by solving an optimization convex problem with constraints, the switched controller is developed to ensure simultaneously the stability of the closed‐loop system and satisfy an optimized upper bound of both the linear quadratic guaranteed cost and the H_∞ norm. Numerical examples are proposed to verify the efficiency and the merits of the method proposed.     

Delay‐dependent H∞ control for singular Markovian jump systems with time delay

The problem of delay‐dependent H_∞ control is considered for singular Markovian jump systems with time delay. The aim of the problem is to design a state feedback controller, which guarantees that the resultant closed‐loop system is not only regular, impulse free and stochastically stable, but also satisfies a prescribed H_∞ performance level for all delays no larger than a given upper bound in terms of linear matrix inequality (LMI) approach. A strict LMI condition is developed to guarantee the existence of the desired state feedback controller. An explicit expression for the desired controller is also given. Numerical examples show the effectiveness of the proposed methods. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust H∞ control for stochastic time‐delayed Markovian switching systems under partly known transition rates and actuator saturation via anti‐windup design

The paper deals with the problem of robust H_∞ control for stochastic time‐delayed Markovian switching systems under partly known transition rates and actuator saturation via anti‐windup design. The problem we address is the design of anti‐windup compensators, which guarantee that the resulting closed‐loop system is robustly stochastically stable with H_∞ performance. By employing local sector conditions and an appropriate Lyapunov–Krasovskii function, sufficient conditions for solving the problem are derived in the form of linear matrix inequalities. Finally, numerical examples are given to demonstrate the validity of the main results. Copyright © 2015 John Wiley & Sons, Ltd.     

Design of robust nonfragile H∞ controller for uncertain nonlinear polynomial systems

This paper is concerned with the robust H_∞ nonfragile controller design for a particular class of nonlinear systems, namely, the perturbed polynomial systems, which are subject to unstructured bounded uncertainties in both the system model and the control law. Combining the Lyapunov stability theory, properties of linear matrix inequality, and Kronecker product properties, a sufficient condition of robust H_∞ nonfragile control design is proposed. More specifically, we propose a robust H_∞ controller of nonlinear polynomial systems with additive unstructured uncertainties and variation in the control law itself that guarantee the stability and the attenuation of external perturbations. Two examples are provided to illustrate the effectiveness of the proposed approach.     

Robust H∞ control for uncertain linear neutral delay systems

This paper deals with the problem of robust H_∞ control for uncertain linear neutral delay systems. The parameter uncertainty under consideration is assumed to be norm‐bounded time‐invariant and appears in all the matrices of the state‐space model. The problem we address is the design of memoryless state feedback controllers such that the closed‐loop system is asymptotically stable and the H_∞ norm of the closed‐loop transfer function from disturbance to the controlled output is strictly less than a prescribed positive scalar for all admissible uncertainties. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the above problem is proposed. When this matrix inequality is feasible, an explicit expression for the desired state feedback controller is given. Furthermore, a numerical example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Robust resilient H ∞ control for stochastic systems with Markovian jump parameters under partially known transition probabilities

In this paper, the robust resilient H _∞ control problem for a class of stochastic systems with partially known transition probabilities is investigated. The system under consideration finds extensive applications because of the uncertainties involved in the system matrices and the general assumption upon the transition probabilities. Attention is focused upon the design of a robust resilient H _∞ state feedback controller, which guarantees the stochastic stability of the closed‐loop system and a prescribed H _∞ disturbance attenuation level for all admissible uncertainties. Sufficient criteria ensuring the stochastic stability and stabilization of the underlying systems are presented via LMIs formulation. A numerical example is provided to demonstrate the effectiveness of all the results. Copyright © 2013 John Wiley & Sons, Ltd.     

Quantized feedback fault‐tolerant H ∞ controller design for linear systems with adaptive mechanism

This paper addresses the design problem of fault‐tolerant H _∞ controller for linear systems with state quantization. By combining linear matrix inequality technique and indirect adaptive method, a new method is proposed to design a fault‐tolerant controller against actuator faults via quantized state feedback. The controller gains are updating according to the online estimation of eventual faults, which are dependent on the quantized state signals. Meanwhile, the proposed designs conditions with variable gains can be proved to be less conservative than those of the traditional controller with fixed gains. A numerical example is presented to illustrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.