H2/H∞ control for stochastic systems with delay

This paper is concerned with the H₂/H_∞ control problem for stochastic linear systems with delay in state, control and external disturbance-dependent noise. A necessary and sufficient condition for the existence of a unique solution to the control problem is derived. The resulting solution is characterised by a kind of complex generalised forward–backward stochastic differential equations with stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the equivalent feedback solution via a new type of Riccati equations. To explain the theoretical results, we apply them to a population control problem.     

H ∞ control for networked systems with random delays and packet dropouts

This paper is concerned with the control problem for a class of systems with random delays and packet dropouts which unavoidably occur during the data transmission in the network. A novel model is developed to describe the random one-step delays and multiple packet dropouts from sensors to controllers and from controllers to actuators by applying four Bernoulli distributed stochastic variables. An observer-based feedback controller is designed via a linear matrix inequality (LMI) approach which guarantees the closed-loop networked system to be exponentially stable in the sense of mean square and also achieves the prescribed H _?? disturbance-rejection-attenuation level. A simulation example shows the effectiveness of the proposed algorithm.     

H∞ output tracking fuzzy control for nonlinear systems with time-varying delay

This paper proposes an observer-based output tracking control via virtual desired reference model for a class of nonlinear systems with time-varying delay and disturbance. First, the Takagi–Sugeno fuzzy model represents the nonlinear system with time-varying delay and disturbance. Then we design an observer to estimate immeasurable states and controller to drive the error between estimated state and virtual desired variables (VDVs) to zero such that the overall control output tracking system has H_∞ control performance. Using Lyapunov–Krasovskii functional, we derive sufficient conditions for stability. The advantages of the proposed output control system are (i) systematic approach to derive VDVs for controller design; (ii) relaxes need for real reference model; (iii) drops need for information of equilibrium; (iv) relaxed condition is provided via three-step procedure to find observer and controller gain. We carry out simulation using a continuous stirred tank reactor system where the effectiveness of the proposed controller is demonstrated by satisfactory numerical results.     

Design of robust H ∞ controller for a half-vehicle active suspension system with input delay

This article is concerned with the problem of robust H _∞ control for a half-vehicle active suspension system with input delay. The delay is assumed to be interval time-varying delay with unknown derivative. The vehicle front sprung mass and the rear unsprung mass are assumed to be varying due to vehicle load variation and may result in parameter uncertainties being modelled by polytopic uncertainty. First of all, regarding the heave and pitch accelerations as the optimisation objectives, and suspension deflection and relative tire load constraints as the output constraints, we build the corresponding suspension systems. Then, by constructing a novel Lyapunov functional involved with the lower and upper bounds of the delay, sufficient condition for the existence of robust H _∞ controller is given to ensure robust asymptotical stability of the closed-loop system and also guarantee the constrained performance. The condition can be converted into convex optimisation problem and verified easily by means of standard software. Finally, a design example is exploited to demonstrate the effectiveness of the proposed design method.     

H ∞ filtering for stochastic systems with time-varying delay

This article considers the problem of H _∞ filter design for stochastic systems with time-varying delay. The time delay is assumed to be of interval type. Attention is focused on the design of delay-dependent filters that guarantee the asymptotic stability in mean square and a prescribed noise attenuation level in an H _∞ sense for the filtering error dynamics. The delay-dependent H _∞ filter design scheme is proposed in terms of a linear matrix inequality. A numerical example is used to illustrate the effectiveness of the proposed approach.     

Delay-dependent H ∞ stabilisation criterion for continuous-time networked control systems with random delays

This article mainly addresses the H _∞ stabilisation problem for a class of networked control systems (NCSs) with random input delays in the continuous-time domain. A Markov jump linear system (MJLS) model with two jump parameters is developed which takes both the sensor-to-controller and controller-to-actuator delays into account. Based on such a MJLS, a new Lyapunov–Krasovskii functional is proposed to establish a delay-dependent H _∞ stabilisation criterion in terms of linear matrix inequalities (LMIs), and a mode-dependent state-feedback controller of NCSs can be determined. Two numerical examples are included to illustrate the derived result.     

Robust H ∞ control for T–S fuzzy systems with time-varying delay

This article focuses on the problem of robust H _∞ control for uncertain T–S fuzzy systems with time-varying delay. By employing a novel technique, new delay-dependent stabilisation conditions for the existence of a robust H _∞ controller are obtained based on the parallel distributed compensation method. The result obtained is an important contribution as it establishes a new way that can reduce the conservatism without imposing any restrictions and computational efforts at the same time. In this article, all the conditions are shown in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using LMI optimisation techniques. Two numerical examples are given to demonstrate the merits of the approach proposed in this article. Finally, application to control a truck-trailer is also given to demonstrate the effectiveness of the proposed design method.     

Distributed consensus observer-based H∞ control for linear systems with sensor and actuator networks

This paper proposed a distributed consensus observer (DCO) based H_∞ control method for a class of linear time-invariant (LTI) continuous systems with a sensor and actuator network (SAN). The communication topology of the SAN under consideration is represented by a directed graph, in which the sensor nodes are not able to acquire all the control inputs applied to the target system from the actuator nodes. To overcome this difficulty, a set of novel DCOs embedded in the sensor nodes and a set of DCO-based controllers embedded in the actuator nodes are initially constructed to estimate and control the state of the target system in a fully distributed way, respectively. The constructed DCOs take full advantage of their consensus property and replace the unavailable control inputs with the approximate ones computed on the basis of the state estimates of the underlying sensor node and its neighboring sensor nodes. Subsequently, a design method of DCO-based H_∞ control is proposed in terms of bilinear matrix inequality (BMI) to ensure that the closed-loop system is exponentially stable while satisfying a prescribed overall H_∞ performance of disturbance attenuation. Moreover, in order to make attenuation level as small as possible, a suboptimal H_∞ control design problem is formulated as a BMI optimization problem, and a modified path-following method is provided for solving this problem by using the existing linear matrix inequality (LMI) optimization techniques. Finally, simulation results demonstrate the effectiveness of the proposed method.     

Robust H∞ control for stochastic systems with nonlinearity,uncertainty and time-varying delay

This paper deals with the problems of robust stochastic stabilization and $H_{\infty }$ control for uncertain stochastic systems with time-varying delay and nonlinear perturbation. System uncertainties are assumed to be norm bounded and time delay is assumed to be bound and time varying with delay-derivative bounded by a constant, which may be greater than one. First, new delay-dependent criterion is proposed by exploiting delay-partitioned Lyapunov–krasovskii functional and by employing tighter integral equalities to estimate the upper bound of the stochastic differential of Lyapunov–krasovskii functional without ignoring some useful terms. Second, based on the criterion obtained, a delay-dependent criterion for the existence of a state feedback $H_{\infty }$ controller that ensures robust stochastic stability and a prescribed $H_{\infty }$ performance level of the closed-loop system for all admissible uncertainties is proposed. These developed results have advantages over some previous ones, in that they involve fewer matrix variables but have less conservatism and they also enlarge the application scope. New sufficient conditions are presented in terms of linear matrix inequality. Numerical examples are used to illustrate the effectiveness and feasibility of the proposed method.     

Dynamic output feedback H ∞ control for networked control systems with quantisation and random communication delays

This article is concerned with the dynamic output feedback H _∞ control problem for networked control systems with quantisation and random communication delays, where the random communication delays from the sensor to the controller and from the controller to the actuator are considered simultaneously. A novel quantised random delay model is proposed, and by using this model, the relationship of the quantisations, delays and the system performance is studied. The quantiser considered here is dynamic and composed of an adjustable zoom parameter and a static quantiser. With the condition on the quantisation range and the error bound satisfied, a quantised H _∞ control strategy is derived such that the closed-loop system is exponentially mean-square stable and with a prescribed H _∞ performance bound. An example is presented to illustrate the effectiveness of the proposed method.     

Sampled-data H ∞ control for networked control systems with digital control inputs

In this article, the problem of sampled-data H _∞ control for networked control systems (NCSs) with digital control inputs is considered, where the physical plant is modelled as a continuous-time one, and the control inputs are discrete-time signals. By exploiting a novel Lyapunov–Krasovskii functional, using the Leibniz–Newton formula and a free-weighting matrix method, sufficient conditions for sampled-data H _∞ performance analysis and H _∞ controller design for such systems are given. Since the obtained conditions of H _∞ controller design are not expressed strictly in term of linear matrix inequalities, the sampled-data H _∞ controller is solved using modified cone complementary linearisation algorithm. In addition, the new sampled-data stability criteria for the NCSs is proved to be less conservative than some existing results. Numerical examples demonstrate the effectiveness of the proposed methods.     

Observer-based H∞ fuzzy control for discrete-time Takagi–Sugeno fuzzy mixed delay systems with random packet losses and multiplicative noises

This paper investigates the observer-based H_∞ fuzzy control problem for a class of discrete-time fuzzy mixed delay systems with random communication packet losses and multiplicative noises, where the mixed delays comprise both discrete time-varying and distributed delays. The random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and multiplicative noises, sufficient conditions for the existence of an observer-based fuzzy feedback controller are derived, such that the closed-loop control system is asymptotically mean-square stable and preserves a guaranteed H_∞ performance. Then a linear matrix inequality approach for designing such an observer-based H_∞ fuzzy controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.     

H ∞ output-feedback LPV control for systems with input saturation

This paper investigates the problem of designing a dynamic H _∞ output-feedback controller under an L _∞ performance representing componentwise input constraints. In order to derive a less conservative stabilization condition therein, this paper introduces a Lyapunov function-based polytopic control law and proposes a method capable of applying the information on interpolation parameters appearing in the procedure of representing saturation nonlinearity as convex polytope. Through this paper, the resultant H _∞/L _∞ problem is efficiently solved based on the set invariance condition formulated in terms of linear matrix inequalities (LMIs).     

Delay-dependent H ∞ control of linear discrete-time systems with an interval-like time-varying delay

The free-weighting-matrix approach is developed to study the H _∞ control of linear discrete-time systems with an interval-like time-varying delay. First, a delay- and range-dependent criterion for a given H _∞ performance is derived. Second, a memoryless H _∞ state-feedback controller is designed based on a performance analysis. Finally, two numerical examples demonstrate the effectiveness of the proposed method and show that both the upper bound and range of an interval-like time-varying delay affect the stability and/or H _∞ performance of a system.     

Decentralised H ∞ control for singular systems

In this article, considering the design problem of decentralised H _∞ controller of singular systems, the two cases of controllers via measurement feedback are designed: one is precise controller, and the other is additive controller gain variation. The design procedures of the two cases of controllers are presented in terms of the solutions to generalised algebraic Riccati inequalities. The designed controllers in each case guarantee that closed-loop singular systems are admissible and with H _∞-norm bound on disturbance attenuation. Finally, a numerical example to demonstrate the validity of the proposed approach is given.     

Robust H ∞ reliable control for a class of uncertain neutral delay systems

This paper deals with the problem of robust reliable control for a class of uncertain neutral delay systems. The aim was to design a state feedback controller such that the plant remained stable for all admissible uncertainties as well as actuator faults among a prespecified subset of actuators or sector-type actuator non-linearity, independently of the delay time. A linear matrix inequality approach was developed to solve the problem addressed with an H X norm bound constraint on disturbance attenuation.     

Quantized H ∞ fault-tolerant control for networked control systems

Quantized H_∞ fault-tolerant control for networked control systems (NCSs) with partial actuator fault with respect to actuators is concerned in this paper. Considering transmission delay, packet dropout and quantization, a synthesis model with partial actuator fault is established. The piecewise constant controller is adopted to model NCS with the transmission delay and packet dropout. Due to data transmitted in practical NCSs should be quantized before they are sent to the next network node, the logarithmic static and time-invariant quantizers at the sensor and controller sides are proposed in the paper. For the established model, an appropriate type of Lyapunov functions is provided to investigate the delay-dependent H_∞ control problem. According to an optimal problem, the controller that makes the system achieve the best performance is designed. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach.