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.     

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.     

An Alternative approach to H∞ control for fuzzy systems

In this paper the problem of H_∞ dynamic feedback control for fuzzy dynamic systems has been studied. First the problem of H_∞ dynamic feedback controller designs for complex nonlinear systems, which can be represented by Takagi‐Sugeno (T‐S) fuzzy systems, is presented. Second, based on a Lyapunov function, four new dynamic feedback H_∞ fuzzy controllers are developed by adequately considering the interactions among all fuzzy sub‐systems and these dynamic feedback H_∞ controllers can be obtained by solving a set of suitable linear matrix inequalities. Finally, two examples are given to demonstrate the effectiveness of the proposed design methods. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

Novel Optimal Design Approach for Output‐Feedback H∞ Control of Vehicle Active Seat‐Suspension System

In this paper, the output‐feedback control problem of a vehicle active seat‐suspension system is investigated. A novel optimal design approach for an output‐feedback H_∞ controller is proposed. The main objective of the controller is to minimize the seat vertical acceleration to improve vehicle ride comfort. First, the human body and the seat are considered in the modeling of a vehicle active suspension system, which makes the model more precise. Other constraints, such as tire deflection, suspension deflection and actuator saturation, are also considered. Then the output‐feedback control strategy is adopted since some state variables, such as body acceleration and body deflection, are unavailable. A concise and effective approach for an output‐feedback H_∞ optimal control is presented. The desired controller is obtained by solving the corresponding linear matrix inequalities (LMIs) and by the calculation of equations proposed in this paper. Finally, a numerical example is presented to show the effectiveness and advantages of the proposed controller design approach.     

H∞ fuzzy static output feedback control of T‐S fuzzy systems based on fuzzy Lyapunov approach

This paper is concerned with the problem of H_∞ fuzzy static output feedback control for discrete‐time Takagi‐Sugeno (T‐S) fuzzy systems, and new design methods are presented. By defining a fuzzy Lyapunov function, a new sufficient condition guaranteeing the H_∞ performance of the T‐S fuzzy systems is derived, and the condition is expressed by a set of linear matrix inequalities. In comparison with the existing literature, the proposed approach may provide more relaxed condition while ensuring better H_∞ performance. The simulation results illustrate the effectiveness of the proposed approach. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Delay‐ and Packet‐Disordering‐Dependent H∞ Output Tracking Control for Networked Control Systems

This paper is concerned with the problem of H_∞ output tracking control for networked control systems (NCSs) with network‐induced delay and packet disordering. Different from the results in existing literature, the controller design in this paper is both delay‐ and packet‐disordering‐dependent. Based on the different cases of consecutive predictions, the networked output tracking system is modeled into a switched system. Moreover, by the corresponding switching‐based Lyapunov functional approach, a linear matrix inequality (LMI)‐based procedure is proposed for designing state‐feedback controllers, which guarantees that the output of the closed‐loop NCSs tracks the output of a given reference model well in the H_∞ sense. In addition, the proposed method can be applied variously due to all kinds of prediction numbers of the consecutive disordering packet have been considered, and the designed controller is based on the prediction case in the last transmission interval, which brings about less conservatism. Finally numerical examples and simulations are used to illustrate the effectiveness and validity of the proposed switching‐based method and the delay‐ and packet‐disordering‐dependent H_∞ output tracking controller design.     

Robust H∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions

In this paper, we present a new scheme for designing a H_∞ stabilizing controller for discrete‐time Takagi‐Sugeno fuzzy systems with actuator saturation and external disturbances. The weighting‐dependent Lyapunov functions approach is used to design a robust static output‐feedback controller. To address the input saturation problem, both constrained and saturated control input cases are considered. In both cases, stabilization conditions of the fuzzy system are formulated as a convex optimization problem in terms of linear matrix inequalities. Two simulation examples are included to illustrate the effectiveness of the proposed design methods. A comparison with the results given in recent literature on the subject is also presented.     

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.     

H∞ Static Output Feedback Control of 2‐D Discrete Systems in FM Second Model

The problem of H_∞ static output feedback (SOF) control of two‐dimensional (2‐D) discrete systems described by the Fornasini‐Marchesini (FM) second model is investigated in this paper. First, by applying the 2‐D Bounded Real Lemma, the 2‐D H_∞ SOF control problem is formulated in terms of a bilinear matrix inequality (BMI). Then, by combining the slack variable technique with two kinds of existing LMI methods, respectively, less conservative sufficient LMI conditions are proposed for the BMI formulation. The relation of these two kinds of LMI conditions are revealed by analyzing the choices of coordinate transformation matrices involved in the first kind of LMI conditions. Finally, a numerical example is provided to demonstrate the effectiveness and merits of the proposed methods.     

Active and Reactive Power Control Techniques Based on Feedback Linearization and Fuzzy Logic for Three‐Phase Grid‐Connected Photovoltaic Inverters

This paper discusses two techniques based on the feedback linearization (FBL) method to control the active and reactive output powers of three‐phase grid‐connected photovoltaic (PV) inverters. The first control scheme is an application of the direct FBL approach. The other is an appropriate combination of the FBL and fuzzy logic (FBL‐FL), and is the main proposed method of this study. Wherein, a unique fuzzy logic controller (FLC) is designed to enhance effectiveness of the linear control method used in the direct FBL. In detail, its major objectives are to improve the transient response and reduce steady‐state oscillations in the output powers. In this research, the illustrative PV inverter utilizes a three‐level DC‐AC converter, an R‐L filter and a 250 V/10 kV wye‐wye transformer to inject the energy, obtained from PV array with a nominal power of 100 kW, into the 10 kV/60Hz three‐phase grid. Numerical simulations in MATLAB and PSIM illustrate that the two FBL‐based structures perform very well in independently regulating the active and reactive output powers to the reference values, even within the parametric uncertainties and the unbalanced grid voltage condition. Moreover, comparisons of simulation results, obtained from the traditional proportional–integral (PI) control and the two FBL‐based structures, show advantages of the proposed FBL‐FL hybrid technique in terms of fast response, small overshoot, acceptable steady‐state fluctuation and high robustness.     

Non-fragile H∞ dynamic output feedback control for uncertain Takagi–Sugeno fuzzy systems with time-varying delay

This paper mainly focuses on the problem of non-fragile H_∞ dynamic output feedback control for a class of uncertain Takagi–Sugeno fuzzy systems with time-varying state delay. Based on a new type of Lyapunov–Krasovskii functional without ignoring any subtle integral terms in the derivatives, a less conservative dynamic output feedback controller with additive gain variations is designed, which guarantees that the closed-loop fuzzy system is asymptotically stable and satisfies a prescribed H_∞-performance level. Furthermore, the obtained parameter-dependent conditions are given in terms of solution to a set of linear matrix inequalities, which improve some existing relevant results. Finally, numerical examples are given to illustrate the effectiveness and merits of the proposed method.     

Decentralised indirect adaptive output feedback fuzzy H ∞ tracking design for a class of large-scale nonlinear systems

A novel decentralised indirect adaptive output feedback fuzzy controller with a compensation controller and an H _∞ tracking controller is presented for a class of uncertain large-scale nonlinear systems in this article. The compensator adaptively compensates for interconnections between subsystems as well as mismatched errors, while the H _∞ controller suppresses the effect of external disturbances. Based upon the combination of fuzzy inference systems, a state observer, H _∞ tracking technique and the strictly positive real condition, the proposed overall observer-based decentralised algorithm guarantees not only asymptotical tracking of reference trajectories but also an arbitrary small attenuation level of the unmodelled error dynamics including the disturbances on the tracking control. Simulation results substantiate the effectiveness of the proposed scheme.     

Mixed Event/Time‐Triggered Static Output Feedback L2‐Gain Control for Networked Control Systems

This paper considers the design of mixed event/time‐triggered controllers for networked control systems (NCSs) under transmission delay and possible packet dropout. Assuming that a conventional delayed static output feedback L₂‐gain controller exists, we propose an output‐based mixed event/time‐triggered communication scheme for reducing the network traffic in a NCS. Moreover, we show that a conventional delayed static output feedback L₂‐gain controller can be obtained by solving a linear matrix inequality with a matrix equality constraint. A numerical example is proposed for demonstrating the theoretical results.     

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.     

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.     

Polynomial static output feedback H∞ control via homogeneous Lyapunov functions

In this paper, we study a polynomial static output feedback (SOF) stabilization problem with H_∞ performance via a homogeneous polynomial Lyapunov function (HPLF). It is shown that the quadratic stability ascertaining the existence of a single constant Lyapunov function becomes a special case. With the HPLF, the proposal is based on a relaxed two‐step sum of square (SOS) construction where a stabilizing polynomial state feedback gain K(x) is returned at the first stage and then the obtained K(x) gain is fed back to the second stage, achieving the SOF closed‐loop stabilization of the underlying polynomial fuzzy control systems. The SOS equations obtained thus effectively serve as a sufficient condition for synthesizing the SOF controllers that guarantee polynomial fuzzy systems stabilization. To demonstrate the effectiveness of the proposed polynomial fuzzy SOF H_∞ control, benchmark examples are provided for the new approach.     

Periodically Time‐Varying Memory State‐Feedback for Robust H2 Control of Uncertain Discrete‐Time Linear Systems

This study is concerned with the synthesis of periodically time‐varying memory state‐feedback controllers (PTVMSFCs) for discrete‐time linear systems. In our preceding studies, we have already established a solid theoretical basis for linear matrix inequality (LMI)‐based (robust) H _∞‐PTVMSFCs synthesis, and the goal of this paper is to extend those results to the H ₂ performance criterion. In the H ₂ case, the main difficulty stems from the fact that we have to ensure the existence of common auxiliary variables for multiple LMI conditions that are related to the Lyapunov inequality and the inequalities for bounding traces that characterize the H ₂ norm. We can overcome this difficulty and derive a necessary and sufficient LMI condition for the optimal H ₂‐PTVMSFC synthesis. On the basis of this result, we also consider robust H ₂‐PTVMSFC synthesis for LTI systems with parametric uncertainties.     

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.     

Reliable control design for composite‐driven scheme based on delay networked T‐S fuzzy system

This paper is focused on reliable controller design for a composite‐driven scheme of networked control systems via Takagi‐Sugeno fuzzy model with probabilistic actuator fault under time‐varying delay. The proposed scheme is distinguished from the other schemes as mentioned in this paper. Aims of this article are to solve the control problem by considering the H_∞, dissipative, and L₂?L_∞ constraints in a unified way. Firstly, to improve the efficient utilization of bandwidth, the adaptive composite‐driven scheme is introduced. In such a scenario, the channel transmission mechanism can be adjusted between adaptive event‐triggered generator scheme and time‐driven scheme. In this study, the threshold is dependent on a new adaptive law, which can be obtained online rather than a predefined constant. With a constant threshold, it is difficult to get the variation of the system. Secondly, a novel fuzzy Lyapunov‐Krasovskii functional is constructed to design the fuzzy controller, and delay‐dependent conditions for stability and performance analysis of the control system are obtained. Then, LMI‐based conditions for the existence of the desired fuzzy controller are presented. Finally, an inverted pendulum that is controlled through the channel is provided to illustrate the effectiveness of the proposed method.