<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> filtering for discrete-time systems with time-varying delay

The problem of H _∞ filtering for discrete-time systems with time-varying delay in measurement is investigated in this paper. First, under the assumption that the time-varying delay is of a known upper bound, the delayed measurement is re-described as the one with multiple state delays. Then the proposed H _∞ filtering problem is transformed into one for systems with multiple measurement channels that contain the same state information as the original measurement and each channel has a single constant delay. Finally, based on the reorganized innovation analysis approach in Krein space, a necessary and sufficient condition for the existence of an H _∞ filter which guarantees a prescribed attenuation level is derived. The solution to the H _∞ filtering is given in terms of the solutions to Riccati and matrix difference equations.     

Mixed <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> filtering for a class of high-speed sampling uncertain systems

The problem of mixed H2/H∞ filtering for polytopic Delta operator systems is investigated. The aim is to design a linear asymptotically stable filter which guarantees that the filtering error system has different performances in different filtering channels. Based on a parameter-dependent Lyapunov function, a new mixed H2/H∞ performance criterion is presented. Upon this performance criterion, a sufficient condition for the full-order mixed H2/H∞ filter is derived in terms of linear matrix inequalities. The filter can be obtained from the solution of a convex optimization problem. The proposed filter design procedure is less conservative than the strategy based on the quadratic stability notion. A numerical example is given to illustrate the feasibility of the proposed approach.     

Robust multi-objective <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> reliable control for delta operator switched uncertain linear systems

This paper deals with the robust guaranteed-cost H _∞ reliable control problem for delta operator switched uncertain linear systems with actuator faults. The upper bound of the guaranteed-cost function is determined and the closed-loop system can be guaranteed some H _∞ performance by using arbitrary and state switching control approaches. Finally, a simulation example is provided to illustrate the efficiency of the proposed methods.     

Mixed <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for linear infinite-dimensional systems

In this paper, we consider mixed H ₂/H _∞ control problems for linear infinite-dimensional systems. The first part considers the state feedback control for the H ₂/H _∞ control problems of linear infinite-dimensional systems. The cost horizon can be infinite or finite time. The solutions of the H ₂/H _∞ control problem for linear infinitedimensional systems are presented in terms of the solutions of the coupled operator Riccati equations and coupled differential operator Riccati equations. The second part addresses the observer-based H ₂/H _∞ control of linear infinite-dimensional systems with infinite horizon and finite horizon costs. The solutions for the observer-based H ₂/H _∞ control problem of linear infinite-dimensional systems are represented in terms of the solutions of coupled operator Riccati equations. The first-order partial differential system examples are presented for illustration. In particular, for these examples, the Riccati equations are represented in terms of the coefficients of first-order partial differential systems.     

Stochastic problems in <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> and <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control

We consider stochastic control systems subjected simultaneously to stochastic and determinate perturbations. Stochastic perturbations are assumed to be state-multiplicative stochastic processes, while determinate perturbations can be any processes with finite energy on infinite time interval. The results of the determinate H _∞-theory are compared to their stochastic analogs. The determinate and stochastic theories are linked together by the lemma that establishes the equivalence between the stability and boundness of the ‖L‖_∞ < γ norm of the perturbation operator L, from one side, and the solvability of certain linear matrix inequalities (LMIs), from the other side. As soon as the stochastic version of the lemma is proven, the γ-controller analysis and design problems are solved, in general, identically in the frame of the united LMI methodology.     

<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> digital redesign for LTI systems

The so-called digital redesign (DR) is a sampled-data (SD) controller design method where an analogue controller is designed firstly, and then transformed to an approximately equivalent digital controller in the sense of state-matching. In this approach, the SD controller is designed by reducing the discrepancy between the discrete-time (DT) counterpart of the closed-loop SD control system and the continuous-time (CT) closed-loop system. In this paper, we develop a DR strategy for CT linear time-invariant systems. More specifically, H _∞ norm of the error dynamic system between the CT and DT plants is minimized for the optimal state-matching performance at every sampling point. The design problem is formulated as linear matrix inequalities which can be efficiently solved by using convex optimization techniques. Finally, an example is given to illustrate the effectiveness of the proposed method.     

Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> consensus control of uncertain multi-agent systems with time delays

This paper is devoted to the robust H _∞ consensus control of multi-agent systems with model parameter uncertainties and external disturbances. In particular, switching networks of multiple agents with general linear dynamics are considered, and uncertain communication delays are also taken into account. It shows that a sufficient condition in terms of linear matrix inequalities (LMIs) is derived for the robust consensus performance with a given H _∞ disturbance attenuation level, and meanwhile the unknown feedback matrix of the proposed distributed state feedback protocol is also determined. A numerical example is included to validate the theoretical results.     

Robust finite-time <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of stochastic jump systems

This paper provides the stochastic finite-time stabilization and H _∞ control problem of Markov jump systems with norm-bounded uncertainties and state delays that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The finite-time H _∞ controller via state feedback is provided to guarantee the stochastic finite-time bounded-ness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible uncertainties and unknown time-delays. The control criterion is formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. Simulation results illustrate the effectiveness of the developed approaches.     

Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for uncertain nonlinear active magnetic bearing systems via Takagi-Sugeno fuzzy models

In this paper, a systematic procedure to design the robust H _∞ fuzzy controller for a nonlinear active magnetic bearing (AMB) system affected by time-varying parametric uncertainties is presented. First, the continuous-time Takagi-Sugeno (T-S) fuzzy model is employed to represent the nonlinear AMB system. Next, based on the obtained fuzzy model, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for robust stability and H _∞ performance of the control system. The main feature of this paper is that some drawbacks existing in the previous approaches such as truncation errors and nonconvex bilinear matrix inequality (BMI) problem are eliminated by utilizing the homogeneous fuzzy model which includes no bias terms in the local state space models rather than the affine one which includes bias terms. Hence, the design method presented here will prove to be more tractable and accessible than the previous ones. Finally, numerical simulations demonstrate the effectiveness of the proposed approach.     

Mixed <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for a class of nonlinear networked control systems

In this paper, the mixed H ₂/H _∞ control problem is investigated for a class of nonlinear discrete-time networked control systems with random network-induced delays, stochastic packet dropouts and probabilistic sensor faults. The packet dropouts process is modeled as a homogeneous Markov chains taking values in a finite state space. Network-induced delays occur in a random way with known upper bound. A set of stochastic variables are exploited to describe sensor faults with different probabilistic density functions. By using a delay-dependent Lyapunov functional, a mode-dependent mixed H ₂/H _∞ controller is designed to guarantee both stochastic stability of the closed-loop system and the prescribed H2, H¥ control performances. Sufficient conditions for the existence of the mixed H ₂/H _∞ controller are presented in terms of a series of LMIs. If these LMIs are feasible, then the modedependent mixed H ₂/H _∞ controller can be obtained. A numerical example is given to demonstrate the effectiveness of the developed method.     

Simultaneous <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> stabilization for chemical reaction systems based on orthogonal complement space

This paper presents a simultaneous H₂/H_∞ stabilization problem for the chemical reaction systems which can be modeled as a finite collection of subsystems. A single dynamic output feedback controller which simultaneously stabilizes the multiple subsystems and captures the mixed H₂/H_∞ control performance is designed. To ensure that the stability condition, the H₂ characterization and the H_∞ characterization can be enforced within a unified matrix inequality framework, a novel technique based on orthogonal complement space is developed. Within such a framework, the controller gain is parameterized by the introduction of a common free positive definite matrix, which is independent of the multiple Lyapunov matrices. An iterative linear matrix inequality (ILMI) algorithm using Matlab Yalmip toolbox is established to deal with the proposed framework. Simulation results of a typical chemical reaction system are exploited to show the validity of the proposed methodology.     

Dynamic output feedback robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of uncertain switched nonlinear systems

The problem of robust H _∞ control problem for a class of switched nonlinear systems with parameter uncertainty is studied by using single Lyapunov function method. The problem under switch-dependent and switch-independent dynamic output feedbacks is solved respectively. Sufficient conditions for solvability of the problem are obtained. The Lyapunov function and the corresponding switching law are explicitly constructed. A numerical example is given to demonstrate the validity of the proposed approach.     

Exponential <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for singular systems with time-varying delay

This paper studies the exponential admissibility and H _∞ control problems for a class of singular systems with time-varying delay in state. Firstly, an exponential admissibility criterion is obtained based on linear matrix inequalities (LMIs). It is worth mentioning that the derivative of the time-varying delay does not need to be smaller than one. Based on the proposed condition, a new delay-dependent H _∞ controller is also given, which guarantees the admissibility and the H _∞ performance γ. Numerical examples are given to illustrate the effectiveness of the proposed method.     

Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> static output feedback control of discrete-time switched polytopic linear systems with average dwell-time

This paper investigates the problem of robust exponential H _∞ static output feedback controller design for a class of discrete-time switched linear systems with polytopic-type time-varying parametric uncertainties. The objective is to design a switched static output feedback controller guaranteeing the exponential stability of the resulting closed-loop system with a minimized exponential H _∞ performance under average dwell-time switching scheme. Based on a parameter-dependent discontinuous switched Lyapunov function combined with Finsler’s lemma and Dualization lemma, some novel conditions for exponential H _∞ performance analysis are first proposed and in turn the static output feedback controller designs are developed. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically efficient with commercially available software. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approaches.     

Delay-dependent approach to robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> filtering for discrete-time singular systems with multiple time-varying delays and polytopic uncertainties

A delay-dependent approach to robust H _∞ filtering is proposed for discrete-time singular systems with multiple time-varying delays and polytopic uncertainties. The delays are interval time-varying delays and uncertainties are a convex compact set of polytopic types. The aim of the designed filter is to guarantee regular, causal, asymptotic stability with H _∞ norm bound of filtering error singular systems. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded lemma (BL) for singular systems with interval time-varying delays is proposed. Based on the result, the existence condition of the robust H _∞ filter and the filter design method are presented in terms of linear matrix inequality (LMI). Finally, two examples are also given to illustrate the effectiveness of the proposed methodology.     

<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> DOF control of stochastic systems with time-varying delay and <Emphasis Type="Italic">L</Emphasis><Subscript>∞</Subscript> disturbance

This paper considers the problem of H _∞ dynamic output feedback (DOF) control for a class of stochastic systems with time-varying delay and L _∞ disturbance. A new delay-dependent sufficient condition for the existence of the DOF controller is derived and the controller design method is given in the form of bilinear matrix inequalities (BMIs). Moreover, a variable step size path-following algorithm is proposed to solve the BMI problem. Numerical examples are given to illustrate the effectiveness of the proposed methods.     

Observer-based <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> guaranteed cost control for uncertain singular time-delay systems with input saturation

In this paper, the problem of observer-based H _∞ guaranteed cost control for uncertain singular timedelay systems with actuator saturation is concerned. A delay-dependent sufficient condition is proposed, which guarantees that the closed-loop system is admissible via Lyapunov theory and linear matrix inequality (LMI) approach. Then, with this condition, the estimation of stability region, the upper bound of cost function and the design method of observer-based H _∞ guaranteed cost controller are given by solving linear matrix inequalities and convex optimization problems. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.     

<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> fault detection for linear singular systems with time-varying delay

This paper deals with the problem of H _∞ fault detection for a kind of linear singular systems with time-varying delay. A generalized form of observer-based fault detection filter (FDF) is first used as a residual generator. Then the design of H _∞-FDF is formulated in the framework of H _∞ filtering. By applying Lyapunov-Kravoskii function approach, delay-dependent conditions on the existence of the H _∞-FDF, which ensure asymptotic stability and a prescribed H _∞ performance level, are derived. With the aid of a cone complementarity linearization technique, an iterative algorithm is proposed to calculate the parameter matrices of the H _∞-FDF in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed algorithm.     

<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of singular systems via delta operator method

This paper studies the problem of state feedback H _∞ control for singular systems through delta operator approach. A necessary and sufficient condition is presented such that a singular delta operator system is admissible with a prescribed H _∞ performance, which can provide a unified framework of the existing H _∞ performance analysis results for both continuous case and discrete case. The existence condition and explicit expression of a desirable H _∞ controller are also obtained for singular delta operator systems. The proposed design method can be used for both singular continuous systems and singular discrete systems directly. The corresponding design procedures, which simplify the classical approaches, are discussed and presented. All obtained conditions in this paper are in the form of strict linear matrix inequalities whose feasible solutions can be found by standard linear programming method. Numerical examples are provided to illustrate the effectiveness of the theoretical results obtained in this paper.