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.     

Composite State Feedback of the Finite Frequency H∞ Control for Discrete‐Time Singularly Perturbed Systems

This paper mainly is concerned with the finite frequency H_∞ control for the discrete‐time singularly perturbed systems. A state feedback controller is designed to stabilize the whole system and to satisfy the desired design specifications. The generalized Kalman–Yakubovich–Popov (GKYP) lemma is used to convert the related frequency domain inequalities in finite frequency ranges to feasible linear matrix inequalities. Based on the Lyapunov stability method, stable conditions are obtained for discrete‐time singularly perturbed systems. A bounded real lemma then is derived, which characterizes the H_∞ norm performance in specific frequency ranges. Furthermore, the approach for the design of a composite state feedback controller is put forward combined with the unique frequency characteristics of singularly perturbed systems. Detailed analysis of the performance achieved by the piecewise composite controller is provided when it is applied to the original system, and the effectiveness and merits of the proposed controller are illustrated with a numerical result.     

State feedback H∞ control for quantized discrete‐time systems

This paper is concerned with the quantized state feedback H_∞ control problem for discrete‐time linear time‐invariant systems. The quantizer considered here is dynamic and composed of an adjustable “zoom” parameter and a static quantizer. Static quantizer ranges are with practical significance and fully considered here. A quantized H_∞ controller design strategy is proposed with taking quantizer errors into account, where an iterative linear matrix inequality (LMI) based optimization algorithm is developed to minimize static quantizer ranges with meeting H_∞ performance requirement for quantized closed‐loop systems. An example is presented to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

STOCHASTIC STABILIZATION AND H∞ CONTROL FOR DISCRETE JUMPING SYSTEMS WITH TIME DELAYS

In this paper, robust stochastic stabilization and H_∞ control for a class of uncertain discrete‐time linear systems with Markovian jumping parameters are considered. Based on a new bounded real lemma derived upon an inequality recently proposed, a new iterative state‐feedback controller design procedure for discrete time‐delay systems is presented. Sufficient conditions for stochastic stabilization are derived in the form of linear matrix inequalities (LMIs) based on an equivalent model transformation, and the corresponding H_∞ control law is given. Finally, numerical examples are given to illustrate the solvability of the problems and effectiveness of the results.     

Event‐triggered output feedback H∞ control for networked control systems

This paper investigates event‐triggered output feedback H_∞ control for a networked control system. Transmitted through a network under an event‐triggered scheme, the sample outputs of the plant are used to drive the dynamical output feedback controller to generate a new control signal in the discrete‐time domain. The discrete‐time control signals are also transmitted through the network to drive the plant. As a result of two types of transmission delays, the controlled plant and the dynamical output feedback controller are driven by the discrete‐time outputs and control signals at different instants of time. An interval decomposition method is introduced to place the controlled plant and the output feedback controller into the same updated time interval but with updated signals at different instants. Based on a proper Lyapunov‐Krasovskii functional, sufficient conditions are derived to ensure H_∞ performance for the controlled plant. Finally, numerical simulations are used to demonstrate the practical utility of the proposed method.     

Resilient H∞ Control Design for Discrete‐Time Uncertain Linear Systems: An Auxiliary System Transformation Approach

This paper studies the resilient (non‐fragile) H∞ output‐feedback control design for discrete‐time uncertain linear systems with controller uncertainty. The design considers parametric norm‐bounded uncertainty in all state‐space matrices of the system, output and controller equations. The paper shows that the resilient H∞ output‐feedback control problem is equivalent to a scaled H∞ output‐feedback control problem of an auxiliary system without any system or controller uncertainty. Using the existing optimal H∞ design to solve the auxiliary system, the design guarantees that the resultant closed‐loop systems are quadratically stable with disturbance attenuation γ for all admissible system and controller uncertainties. A numerical example is given to illustrate the design method and its benefits.     

Robust H∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching

This paper is concerned with the problems of robust stochastic stabilization and robust H_∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching. The parameter uncertainties are time‐varying norm‐bounded. For the robust stochastic stabilization problem, the purpose is the design of a state feedback controller which ensures the robust stochastic stability of the closed‐loop system irrespective of all admissible parameter uncertainties; while for the robust H_∞ control problem, in addition to the robust stochastic stability requirement, a prescribed level of disturbance attenuation is required to be achieved. Sufficient conditions for the solvability of these problems are obtained in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, explicit expressions of the desired state feedback controllers are also given. An illustrative example is provided to show the effectiveness of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Output Feedback H∞ Control for Discrete‐time Mean‐field Stochastic Systems

This paper is to consider dynamic output feedback H_∞ control of mean‐field type for stochastic discrete‐time systems with state‐ and disturbance‐dependent noise. A stochastic bounded real lemma (SBRL) of mean‐field type is derived. Based on the SBRL, a sufficient condition with the form of coupled nonlinear matrix inequalities is derived for the existence of a stabilizing H_∞ controller. Moreover, a numerical example is given to examine the effectiveness of the theoretical results.     

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∞Fuzzy State‐Feedback Control Plus State‐Derivative‐Feedback Control Synthesis for Photovoltaic Systems

This paper addresses the problem of designing an H_∞fuzzy state‐ feedback (SF) plus state‐derivative‐feedback (SDF) control system for photovoltaic (PV) systems based on a linear matrix inequality (LMI) approach. The TS fuzzy controller is designed on the basis of the Takagi‐Sugeno (TS) fuzzy model. The sufficient condition is found such that the system with the fuzzy controller is asymptotically stable and an H_∞performance is satisfied. First, a dc/dc buck converter is considered to regulate the power output by controlling state and state‐derivative variables of PV systems. The dynamic model of PV systems is approximated by the TS fuzzy model in the form of nonlinear systems. Then, based on a well‐known Lyapunov functional approach, the synthetic is formulated of an H_∞fuzzy SF plus SDF control law, which guarantees the L₂‐gain from an exogenous input to the regulated output to be less than or equal to some prescribed value. Finally, to show effectiveness, the simulation of the PV systems with the proposed control is assessed by the computer programme. The proposed control method shows good performance for power output and high stability for the PV system.     

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.     

H∞ control for discrete‐time Markovian jump systems with partial information on transition probabilities

This paper focuses on mode‐dependent H_∞ state‐feedback control for a class of discrete‐time Markovian jump systems (MJSs) with partial information on transition probabilities (TPs). The augmented free‐connection weighting matrices are introduced by considering the influence of partial information of TPs on discrete‐time MJSs and the disturbance input on the state vector. As a result, the less conservative stability criterion and bounded real lemma (BRL) of MJSs with partly unknown TPs are obtained. Then the sufficient conditions for designing the mode‐dependent H_∞ controllers are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness and the merits of the proposed method.     

Finite‐time H∞ bumpless transfer control for switched systems: A state‐dependent switching approach

This paper addresses the finite‐time H_∞ bumpless transfer control problem for switched systems. The main idea lies in designing a state‐feedback controller with amplitude limitation and a state‐dependent switching law to reduce control bumps caused by switching. First, a local bumpless transfer condition is proposed to limit the amplitude of switching controllers at switching points. Second, by introducing a state‐dependent switching law, a prescribed finite‐time H_∞ bumpless transfer control performance is attained even if it does not hold for each subsystem or system state remaining on a switching surface. Third, a sufficient condition verifying the solvability of finite‐time H_∞ bumpless transfer control problem is established by resorting to multiple Lyapunov function method. Finally, the effectiveness of developed method is illustrated by a numerical example.     

H∞ output feedback control for stochastic systems with randomly occurring convex‐bounded uncertainties and channel fadings

In this paper, the H_∞ output feedback control problem for a class of stochastic discrete‐time systems with randomly occurring convex‐bounded uncertainties and channel fadings is investigated. A sequence of mutually independent random variables with known probabilistic distributions are utilized to describe the randomness that convex‐bounded uncertainties appear in practical systems. The measurements with channel fadings are given by a stochastic Rice fading model which is regulated by a set of random variables with certain probability density functions. The purpose of this paper is to design an output feedback controller such that the closed‐loop control system is asymptotically stable with a prescribed H_∞ performance level. The less conservative results are obtained by employing the stochastic Lyapunov technique. Numerical examples are presented to illustrate effectiveness of the proposed approach.     

Robust H∞ control for a class of quasi‐linear uncertain stochastic time‐varying delayed systems

This paper studies the H_∞ control for a class of quasi‐linear uncertain stochastic time‐varying delayed systems. Firstly, by using the linear matrix inequality (LMI) method, a sufficient condition is obtained for the robustly stochastic stability. Secondly, the robust H_∞ state feedback controller is designed, such that the considered system is not only internally stochastically stabilizable but also satisfies the robust H_∞ performance. The desired robust H_∞ controller is obtained via solving some LMIs. Finally, one example is provided to demonstrate the effectiveness of the proposed method.     

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.     

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.     

STABILIZATION AND H∞ CONTROL FOR UNCERTAIN STOCHASTIC TIME‐DELAY SYSTEMS VIA NON‐FRAGILE CONTROLLERS

This paper considers the problems of robust non‐fragile stochastic stabilization and H_∞ control for uncertain time‐delay stochastic systems with time‐varying norm‐bounded parameter uncertainties in both the state and input matrices. Attention is focused on the design of memoryless state feedback controllers which are subject to norm‐bounded uncertainties. For both the cases of additive and multiplicative controller uncertainties, delay‐independent sufficient conditions for the solvability of the above problems are obtained. The desired state feedback controller can be constructed by solving a certain linear matrix inequality.     

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.