LMI OPTIMIZATION APPROACH FOR DELAY‐DEPENDENT H∞ CONTROL OF TIME‐VARYING DELAY SYSTEMS

In this paper, the robust delay‐dependent H_∞ control for a class of uncertain systems with time‐varying delay is considered. An improved state feedback H_∞ control is proposed to minimize the H_∞‐norm bound via the LMI optimization approach. Based on the proposed result, delay‐dependent criteria are obtained without using the model transformation technique or bounded inequalities on cross product terms. The linear matrix inequality (LMI) optimization approach is used to design the robust H_∞ state feedback control. Some numerical examples are given to illustrate the effectiveness of the approach.     

H∞ control for discrete‐time nonlinear switching systems

This paper formulates and solves the robust H^∞ control problem for discrete‐time nonlinear switching systems. The H^∞ control problem is interpreted as the l₂ finite gain control problem and is studied using a dissipative systems theory for switched systems. Both state and measurement feedback control problems are formulated as dynamic games and solved using dynamic programming. The partially observed dynamic game corresponding to the measurement feedback control problem is solved by transforming into a completely observed, full state infinite‐dimensional game problem using information states. Our results are illustrated with an example. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust Reliable H∞ Control for Discrete‐Time Systems with Actuator Delays

This article focuses on the robust state feedback reliable H_∞ control problem for discrete‐time systems. Discrete‐time systems with time‐varying delayed control input are formulated. Based on the Lyapunov–Krasovskii method and linear matrix inequality (LMI) approach, delay‐dependent sufficient conditions are developed for synthesizing the state feedback controller for an uncertain discrete‐time system. The parameter uncertainty is assumed to be norm bounded. A design scheme for the state feedback reliable H_∞ controller is proposed in terms of LMIs, which can guarantee the global asymptotic stability and the minimum disturbance attenuation level. Finally, numerical examples are provided to illustrate the effectiveness and reduced conservatism of the proposed methods.     

A new finite sum inequality approach to delay‐dependent H∞ control of discrete‐time systems with time‐varying delay

This paper deals with delay‐dependent H_∞ control for discrete‐time systems with time‐varying delay. A new finite sum inequality is first established to derive a delay‐dependent condition, under which the resulting closed‐loop system via a state feedback is asymptotically stable with a prescribed H_∞ noise attenuation level. Then, an iterative algorithm involving convex optimization is proposed to obtain a suboptimal H_∞ controller. Finally, two numerical examples are given to show the effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust H∞ Control Problem For General Nonlinear Systems With Uncertainty

In this paper, both state and output feedback robust H^∞ control problems for general nonlinear systems with norm‐bound uncertainty are considered. Sufficient conditions for the existence of robust output feedback H^∞ controller are provided. State space formulas for robust H^∞ output controller are provided.     

Simultaneous robust normalization and delay‐dependent robust H∞ stabilization for singular time‐delay systems with uncertainties in the derivative matrices

This paper investigates the problem of simultaneous robust normalization and delay‐dependent H_∞ control for a class of singular time‐delay systems with uncertainties. Not only the state and input matrices but also the derivative matrices of the considered systems are assumed to have uncertainties. New sufficient conditions for the existence of a proportional plus derivative state feedback H_∞ controller are derived as LMIs such that the closed‐loop singular system is normal, stable, and guarantee a specific level of performance. Specially, a static state feedback H_∞ controller alone or a state‐derivative feedback H_∞ controller alone can unite to be dealt with by applying our proposed method. Two simulation examples are provided to demonstrate the effectiveness of the proposed approach in this paper. Copyright © 2014 John Wiley & Sons, Ltd.     

Delay‐dependent robust H∞ control for uncertain stochastic time‐delay systems

This paper investigates the robust H_∞ control problem for stochastic systems with a delay in the state. Sufficient delay‐dependent conditions for the existence of state‐feedback controllers are proposed to guarantee mean‐square asymptotic stability as well as the prescribed H_∞ performance for the closed‐loop systems. Moreover, the results are further extended to the stochastic time‐delay systems with parameter uncertainties, which are assumed to be time‐varying norm‐bounded appearing in both the state and the input matrices. The appealing idea is to partition the delay, which differs greatly from the most existing results and reduces conservatism by thinning the delay partitioning. Numerical examples are provided to show the advantages of the proposed techniques. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust H∞ output‐feedback control of retarded state‐multiplicative stochastic systems

Linear, state‐delayed, continuous‐time systems are considered with both stochastic and norm‐bounded deterministic uncertainties in the state–space model. The problem of robust dynamic H_∞ output‐feedback control is solved, for the stationary case, via the input–output approach where the system is replaced by a nonretarded system with additional deterministic norm‐bounded uncertainties. A delay‐dependent result is obtained which involves the solution of a simple linear matrix inequality. In this problem, a cost function is defined which is the expected value of the standard H_∞ performance cost with respect to the stochastic parameters. A practical example taken from the field of guidance control is given that demonstrates the applicability of the theory. Copyright © 2010 John Wiley & Sons, Ltd.     

网络环境下不确定时滞系统鲁棒H∞控制

研究了网络环境下不确定时滞系统的鲁棒 H∞ 控制器的设计问题. 在综合考虑网络的非理想状况下, 建立一种新的网络控制模型. 然后利用 Lyapunov Krsasovskii 泛函方法,通过引入自由矩阵, 得到网络控制系统的 H∞ 鲁棒稳定条件和相应的鲁棒 H∞ 时滞状态反馈控制器的设计方法. 实例表明了本文所得结果的有效性.     

Robust H∞ control for uncertain singular systems with state delay

This paper addresses the problem of robust H_∞ control for uncertain continuous singular systems with state delay. The singular system under consideration involves state time delay and time‐invariant norm‐bounded uncertainty. Based on the linear matrix inequality (LMI) approach, we design a memoryless state feedback controller law, which guarantees that, for all admissible uncertainties, the resulting closed‐loop system is not only regular, impulse free and stable, but also meets an H_∞‐norm bound constraint on disturbance attenuation. A numerical example is provided to demonstrate the applicability of the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

Finite horizon H∞ control for a class of sampled‐data linear quantum systems

In this paper, a finite horizon H^∞ control problem is solved for a class of linear quantum systems using a dynamic game approach for the case of sampled‐data measurements. The methodology adopted involves an equivalence between the quantum problem and two auxiliary classical problems. Copyright © 2016 John Wiley & Sons, Ltd.     

H∞ output tracking control for uncertain networked control systems via a switched system approach

In this paper, the problem of H_∞ output tracking control for networked control systems with random time delays and system uncertainties is investigated. Effective sampling instant that is tightly related with transmission delay from sensor to actuator is proposed to ensure that the random variable time delay is always shorter than one effective sampling period. By using both active time‐varying sampling period strategy and hybrid node‐driven mechanism, the switching instant is coincided with the effective sampling instant. An augmented time‐varying networked tracking system model is provided by including the output tracking error as an additional state. However, random transmission delay causes indeterminate sampling period, which induces infinite subsystems. Gridding approach is introduced to transform the continuous time axis into discrete‐time sequences, which guarantees the finite number of switching rules. By employing multiple Lyapunov–Krasovskii functions, linear matrix inequality (LMI)‐based output tracking H_∞ performance analysis is presented, and robust switching H_∞ model reference tracking controller for networked control systems with communication constraints and system uncertainties is designed to guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. Finally, simulation results illustrate the correctness and effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust stabilization and H∞ control of uncertain stochastic time‐delay systems with nonlinear perturbation

This paper investigates the problem of delay‐dependent robust stochastic stabilization and H_∞ control for uncertain stochastic nonlinear systems with time‐varying delay. System uncertainties are assumed to be norm bounded. Firstly, by using novel method to deal with the integral terms, robustly stochastic stabilization results are obtained for stochastic uncertain systems with nonlinear perturbation, and an appropriate memoryless state feedback controller can be chosen. Compared with previous results, the new technique can sufficiently utilize more negative items information. Then, robust H_∞ control for uncertain stochastic system with time‐varying delay and nonlinear perturbation is considered, and the controller is designed, which will guarantee that closed‐loop system is robustly stochastically stable with disturbance attenuation level. Finally, two numerical examples are listed to illustrate that our results are effective and less conservative than other reports in previous literature. Copyright © 2016 John Wiley & Sons, Ltd.     

NETWORK‐INDUCED DELAY‐DEPENDENT H∞ CONTROLLER DESIGN FOR A CLASS OF NETWORKED CONTROL SYSTEMS

This paper is concerned with the problem of robust H_∞ controller design for a class of uncertain networked control systems (NCSs). The network‐induced delay is of an interval‐like time‐varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be normbounded and possibly time‐varying. Based on Lyapunov‐Krasovskii functional approach, a robust H_∞ controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay‐dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H_∞ performance level of the closed‐loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method.     

Robust H∞ Control for Non‐Minimum Phase Switched Cascade Systems with Time Delay

The H_∞ control of a class of the uncertain switched nonlinear cascaded systems with time delay is explored in this paper via the multiple Lyapunov functions. The considered systems are assumed to comprise an inherently nonlinear and a linearizable nonlinear dynamic system that may be non‐minimum phase. A group of partial differential inequalities containing adjustable functions are used in the control design task. The state feedback controllers and a suitable switching law are designed simultaneously so as to achieve the desired disturbance attenuation while preserving asymptotic stability for all admissible uncertainties. The partial differential inequalities are of lower dimension than general Hamilton–Jacobi inequalities, and therefore the solving process is feasible. This particular technique is applicable even if no subsystem is asymptotically stable. The non‐minimum phase property is compensated for by means of an appropriate switching mechanism. A robust H_∞ control for non‐switched cascade system with time delay is obtained in addition. An illustrative example is given to demonstrate the efficiency of the proposed design method.     

Quadratic stabilizability and H∞ control of linear discrete‐time stochastic uncertain systems

This paper considers quadratic stabilizability and H_∞ feedback control for stochastic discrete‐time uncertain systems with state‐ and control‐dependent noise. Specifically, the uncertain parameters considered are norm‐bounded and external disturbance is an l²‐square summable stochastic process. Firstly, both quadratic stability and quadratic stabilization criteria are presented in the form of linear matrix inequalities (LMIs). Then we design the robust H_∞ state and output feedback H_∞ controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H_∞ controllable. Sufficient conditions for the existence of the desired robust H_∞ controllers are obtained via LMIs. Finally, some examples are supplied to illustrate the effectiveness of our results.     

H∞ boundary control for a class of nonlinear stochastic parabolic distributed parameter systems

This paper addresses the problem of H_∞ boundary control for a class of nonlinear stochastic distributed parameter systems expressed by parabolic stochastic partial differential equations (SPDEs) of Itô type. A simple but effective H_∞ boundary static output feedback (SOF) control scheme with collocated boundary measurement is introduced to ensure the local exponential stability in the mean square sense with an H_∞ performance. By using the semigroup theory, the disturbance‐free closed‐loop well‐posedness analysis is first given. Then, based on the SPDE model, a general linear matrix inequality based H_∞ boundary SOF control design is provided via Lyapunov technique and infinite‐dimensional infinitesimal operator, such that the disturbance‐free closed‐loop system is locally exponentially stable in the mean square sense and the H_∞ performance of disturbance attenuation can also be achieved in the presence of disturbances. Finally, simulation results on a stochastic Fisher‐Kolmogorov‐Petrovsky‐Piscounov equation illustrate the effectiveness of the proposed method.     

Delay‐dependent adaptive reliable H∞ control of linear time‐varying delay systems

This paper considers the problem of delay‐dependent adaptive reliable H_∞ controller design against actuator faults for linear time‐varying delay systems. Based on the online estimation of eventual faults, the parameters of adaptive reliable H_∞ controller are updating automatically to compensate the fault effects on the system. A new delay‐dependent reliable H_∞ controller is established using a linear matrix inequality technique and an adaptive method, which guarantees the stability and adaptive H_∞ performance of closed‐loop systems in normal and faulty cases. A numerical example and its simulation results illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Time delay and packet dropout compensation for networked control systems: a linear estimation method

This article studies the problem of H _∞ controller design for networked control systems (NCSs) with time delay and packet dropout. A linear estimation-based time delay and packet dropout compensation method is proposed. The delay switching-based method is presented to deal with the variation of time delay, and H _∞ controller design is presented for NCSs with packet dropout compensation by using linear matrix inequality (LMI)-based method. Then the combined delay switching and parameter uncertainty-based method is presented to model the variation of time delay, and H _∞ controller design is also presented. The simulation results illustrate the effectiveness of the newly proposed linear estimation-based time delay and packet dropout compensation.     

Robust mixed H2/H∞ delayed state feedback control of uncertain neutral systems with time‐varying delays

This paper considers the problem of robust mixed H₂/H_∞ delayed state feedback control for a class of uncertain neutral systems with time‐varying discrete and distributed delays. Based on the Lyapunov–Krasovskii functional theory, new required sufficient conditions are established in terms of delay‐range‐dependent linear matrix inequalities for the stability and stabilization of the considered system using some free matrices. The desired robust mixed H₂/H_∞ delayed state feedback control is derived based on a convex optimization method such that the resulting closed‐loop system is asymptotically stable and satisfies H₂ performance with a guaranteed cost and a prescribed level of H_∞ performance, simultaneously. Finally, a numerical example is given to illustrate the effectiveness of our approach. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society