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.     

<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.     

<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> 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.     

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.     

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.     

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.     

Adaptive robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of time delay systems with unknown uncertainty bounds

The problem of adaptive robust H _∞ control for uncertain systems with multiple delays is considered in this paper. The essential requirement for the uncertainties is that they satisfy matching conditions and are norm-bounded, but the bounds are not necessarily known. The objective is to design adaptive robust H _∞ state-feedback controller such that the resulting closed-loop system is asymptotically stable and a prescribed H _∞ performance level of the closed loop system for disturbance attenuation is guaranteed. To solve this problem, a new sufficient condition is presented in terms of a linear matrix inequality (LMI). The effectiveness of proposed method is verified by its application to an unstable system.     

<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 exponential <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for autonomous platoon against actuator saturation and time-varying delay

This paper is concerned with bidirectional autonomous platoon control with saturating actuator and time-varying delay. First, A new bidirectional platoon control system model is established, in which the effect of engine time uncertainty, actuator saturation and time-varying actuator delay is involved. Then, the robust exponential stability conditions of the platoon system are presented, only use information from its immediate neighbors. The theoretical results show that the proposed platoon controller would be able to safely maintain a smaller inter-vehicle spacing, less fuel and would be bidirectional string stable. Finally, some numerical simulations are provided to demonstrate the effectiveness and advantage of the presented methodology.     

Delay-dependent <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for jumping delayed systems with two Markov processes

This paper addresses the H _∞ control problem for jumping delayed systems with two separable Markov processes. The objective is to design a controller such that the resulting closed-loop system is exponentially mean-square stable with a given decay rate and satisfies a prescribed H _∞ performance level. A decay-rate-dependent condition is obtained for the existence of admissible controllers in term of linear matrix inequalities. Two numerical examples are presented to demonstrate the effectiveness of the proposed method.     

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.     

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.     

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.     

<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for sochastic time-delayed Markovian switching systems with partly known transition rates and input saturation

The paper is concerned with the problem of H _∞ control for stochastic time-delayed Markovian switching systems with partly known transition rates and input saturation. By employing more appropriate Lyapunov- Krasovskii functional, a state feedback controller is designed to guarantee stochastic stability of the corresponding closed-loop system with H _∞ performance. A linear matrix inequality approach is employed to obtain the controller gain matrix. Two illustrative examples are provided to show the potential of the proposed techniques.     

<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.     

<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of networked control systems with packet disordering with an improved prediction-based method

This paper is concerned with H _∞ control of networked control systems (NCSs) with both network-induced delay and packet disordering taken into account. A switching-based method depends on different cases of prediction numbers is presented to model the NCSs as a switched system. With the application of an improved prediciton-based method to compensate for the time delay and packet disordering, H _∞ controller is designed by solving the linear matrix inequalities (LMIs). The proposed method can be applied variously due to all kinds of prediciton numbers of the consective disordering packet have been considered, which means that our techniques are less conservative than existing literatures. Finally numerical examples and simulations are used to illustrate the effectiveness and validity of the proposed switching-based method and the improved prediction-based H _∞ controller design synthesis.     

Discontinuous <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of underactuated mechanical systems with friction and backlash

Nonlinear H _∞-control is extended to discontinuous mechanical systems with degree of underactuation one, where nonlinear phenomena such as Coulomb friction and backlash are considered. The problem in question is to design a feedback controller via output measurements so as to obtain the closed-loop system in which all trajectories are locally ultimate bounded, and the underactuated link is regulated to a desired position while also attenuating the influence of external perturbations and nonlinear phenomena. It is considered that positions are the only measurements available for feedback in the system. Performance issues of the discontinuous H _∞-regulation controller are illustrated in an experimental study made for a rectilinear plant with friction modified to have a gap in the point of contact between bodies.