State and Unknown Input H∞ Observers for Discrete‐Time LPV Systems

This paper proposes state and unknown input (UI) observers for linear parameter varying (LPV) systems affected by UI and perturbations in both state and measurement equations. The estimation is done by minimizing the L₂ transfer between the perturbations and the state estimation error (H_∞‐observation). The originality of the paper is to provide a generalization of existing works, specially by relaxing an assumption on systems matrices, widely used for UI decoupling. After giving the main results, some examples illustrate the theoretical contributions and give comparisons to former publications.     

H∞ Control for Continuous‐Time Mean‐Field Stochastic Systems

An H_∞‐type control is considered for mean‐field stochastic differential equations (SDEs) in this paper. A stochastic bounded real lemma (SBRL) is proved for mean‐field stochastic continuous‐time systems with state‐ and disturbance‐dependent noise. Based on SBRL, a sufficient condition is given for the existence of a stabilizing H_∞ controller in terms of coupled nonlinear matrix inequalities.     

Adaptive H∞ Control of Piecewise‐Linear Systems with Parametric Uncertainties and External Disturbances

In this paper, we study the adaptive H_∞ control problem for piecewise linear systems with parametric uncertainties and external disturbances. Motivated by the vector projection technique and dissipation theory, we propose a piecewise H_∞ controller and its associated projection‐type parameter adaptation law, which are capable of guaranteeing the system stability and minimizing the effect of disturbances. Moreover, the common quadratic Lyapunov function method is used such that all of the synthesis conditions are formulated as linear matrix inequities and thus can be solved efficiently. Finally, a numerical example is provided to illustrate the results.     

Finite‐Time H∞ Filtering for Nonlinear Continuous‐Time Singular Semi‐Markov Jump Systems

The stochastic finite‐time H_∞ filtering issue for a class of nonlinear continuous‐time singular semi‐Markov jump systems is discussed in this paper. Firstly, sufficient conditions on singular stochastic H_∞ finite‐time boundedness for the filtering error system are established. The existence of a unique solution for the corresponding system is also ensured. Secondly, based on the bounds of the time‐varying transition rate, without imposing constraints on slack variables, a novel approach to finite‐time H_∞ filter design is proposed in the forms of strict LMIs, which guarantees the filtering error system is singular stochastic H_∞ finite‐time bounded and of a unique solution. Compared with the existing ones, the presented results reveal less conservativeness. Finally, one numerical example is exploited to testify the advantage of the proposed design technique.     

H∞ Control of Linear Discrete‐Time Systems With Norm‐Bounded Nonlinear Uncertainties

In this paper, robust H_∞ control of a class of discrete‐time uncertain systems in state‐space form with linear nominal parts and norm‐bounded nonlinear uncertainties in both state and output equations is discussed. Such systems have a unique characterisic; that is, the two norm‐bounded nonlinear uncertainties have the equivalent representation by means of time‐varying and norm‐bounded linear uncertainties. To overcome the conservativenss of [5], the two nonlinear uncertainty sets are considered to be different. Then, by converting such systems into related discrete‐time linear systems with time‐varying and norm‐bounded linear uncertainties, we obtain that a sufficient condition for robust H_∞ control of such systems is equivalent to the solvability of the same problem of the related linear uncertain systems, which is solvable by means of a linear algebraic Riccati inequality.     

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.     

H∞ Control for a Class of Continuous‐time Switched Systems with State Constraints

This paper investigates the H_∞ control problem for a class of continuous‐time switched systems subject to state constraints with an improved average dwell time. The state constraints are converted into state saturations by limiting the state in a unit hypercube. By employing this proposed improved average dwell time method, which takes into account different decay rates of a Lyapunov function related to an active subsystem according to whether the saturations occur or not, the resulting minimum of admissible average dwell time is smaller than the one of the standard average dwell time, which only considers the same decay rate regardless of whether the saturations occur or not. In addition, switched state feedback controllers are designed such that the closed‐loop switched system, subject to state constraints, is asymptotically stable and achieves a weighted L₂‐gain. Sufficient conditions for H_∞ control of the switched system with state constraints are derived before an application to a Pulse‐Width‐Modulation (PWM)‐driven boost converter is given to illustrate the applicability and the effectiveness of the proposed 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.     

PID controller optimization for H∞ control by linear programming

The constraints on the PID gains, which are derived from the H_∞ norm performance index by discretization of the frequency, are convex or concave depending on frequencies. This problem is a non‐convex problem, and a new method of approximating these constraints as adequate linear inequalities is proposed. Then, the optimal solution can be efficiently and successfully searched for by applying linear programming iteratively. This method is compared with methods based on barrier function and linear matrix inequality. Copyright © 2000 John Wiley & Sons, Ltd.     

Robust Finite‐Time H∞ Control of a Class of Disturbed Systems using Lmi‐Based Approach

In this paper, the definition of robust finite‐time H_∞ control is presented for a class of disturbed systems. Time‐varying norm‐bounded exogenous disturbance is considered in the system. A state feedback controller is designed, via a Linear Matrix Inequalities (LMIs) approach, which ensures that the closed‐loop system is finite‐time bounded (FTB) and reduces the effect of the disturbance input on the controlled output to a prescribed level. The main result, derived by Lyapunov functions, is a sufficient condition for FTB of disturbed systems and the sufficient condition can be reduced to a feasibility problem involving LMIs. Then a DC motor position control problem is simulated as a demonstration for this study. Simulation results are presented to show the effectiveness of the proposed method as a promising approach for controlling similar disturbed systems.     

Time domain constrained H∞‐synthesis

Structured H_∞‐synthesis subject to time domain performance specifications is introduced. Our method allows to control trajectories of the linearized system and the underlying nonlinear dynamics simultaneously. A non‐smooth bundle optimization method for this class of programs is proposed and discussed. Our approach is tested against two benchmark studies: control of a rotational actuator to attenuate vibration noise, and control of a continuous crystallizer. Our algorithm gives a local convergence certificate and is suited for systems with large state dimension. Copyright © 2010 John Wiley & Sons, Ltd.     

H∞ Control with Transients for Singular Systems

In this paper, the problem of a generalized type of H_∞ control is investigated for continuous‐time singular systems, which treats a mixed attenuation of exogenous inputs and initial conditions. First, a performance measure that is essentially the worst‐case norm of the regulated outputs over all exogenous inputs and initial conditions is introduced. A necessary and sufficient condition is obtained to ensure the singular system to be admissible and the performance measure to be less than a prescribed scalar. Based on the criterion a sufficient condition for the existence of a state‐feedback controller is established in terms of linear matrix inequalities. Moreover, the relationship between the performance measure and the standard H_∞ norm of the system is provided. Two numerical examples are given to demonstrate the properties of the obtained results.     

Quantized H∞ Control for Networked Systems with Communication Constraints

The problem of quantized H_∞ control for networked control systems (NCSs) subject to time‐varying delay and multiple packet dropouts is investigated in this paper. Both the control input and the measurement output signals are quantized before being transmitted and the quantized errors are described as sector bound uncertainties. The measurement channel and the control channel packet dropouts are considered simultaneously, and the stochastic variables satisfying Bernoulli random binary distribution are utilized to model the random multiple packet dropouts. Sufficient conditions for the existence of an observer‐based controller are established to ensure the exponential mean‐square stablility of the closed‐loop system and achieve the optimal H_∞ disturbance attenuation level. By using a globally convergent algorithm involving convex optimization, the nonconvex feasibility can be solved successfully. Finally, a numerical example is given to illustrate the effectiveness and applicability of the proposed 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.     

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.     

Singular H∞ control for nonlinear systems

This paper presents a solution to the singular H_∞ control problem via state feedback for a class of nonlinear systems. It is shown that the problem of almost disturbance decoupling with stability plays a fundamental role in the solution of the considered problem. We also point out when the singular problem can be reduced to a regular one or solved via standard H_∞ technique. We must stress that the solution of the singular problem is obtained without making any approximation of it by means of regular problems. © 1997 John Wiley & Sons, Ltd.     

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 and Sliding Mode Control of Magnetic Levitation System

In this paper, H∞ disturbance attenuation control and sliding mode disturbance estimation and compensation control of a magnetic levitation system are studied. A magnetic levitation apparatus is established, and its model is measured. Then the system model is feedback linearized. A H∞ controller is then designed. For comparison, a sliding mode controller and a PID controller also were designed. Some experiments were performed to compare the performance of the H∞ controller, the sliding mode controller and the PID controller.     

H∞ CONTROL FOR DELAYED DISCRETE FUZZY SYSTEMS

In this paper, the H∞ controller design for discrete‐time fuzzy systems with time‐delay is investigated. An improved Lyapunov‐ Krasovskii function which is explicitly dependent on the membership functions is proposed to obtain less conservative results. The controller design problem can be cast into a set of linear matrix inequalities. Finally, a simulation example is given to show the effectiveness of the proposed design approaches.     

H∞ estimation for uncertain systems

This paper deals with the problem of H_∞ estimation for linear systems with a certain type of time-varying norm-bounded parameter uncertainty in both the state and output matrices. We address the problem of designing an asymptotically stable estimator that guarantees a prescribed level of H_∞ noise attenuation for all admissible parameter uncertainties. Both an interpolation theory approach and a Riccati equation approach are proposed to solve the estimation problem, with each method having its own advantages. The first approach seems more numerically attractive whilst the second one provides a simple structure for the estimator with its solution given in terms of two algebraic Riccati equations and a parameterization of a class of suitable H_∞ estimators. The Riccati equation approach also pinpoints the ‘worst-case’ uncertainty.