H∞ control of periodic piecewise polynomial time-varying systems with polynomial Lyapunov function

In this paper, the H_∞ control problem of periodic piecewise systems with polynomial time-varying subsystems is addressed. Based on a periodic Lyapunov function with a continuous time-dependent Lyapunov matrix polynomial, the H_∞ performance is studied. The result can be easily reduced to the conditions for periodic piecewise systems with constant subsystems or linear time-varying systems based on a common Lyapunov function or a linear time-varying Lyapunov matrix. Moreover, an H_∞ controller with time-varying polynomial controller gain is proposed as well, which could be directly solved with the linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the proposed method.     

Finite-horizon H∞ consensus control for multi-agent systems under energy constraint

In this paper, a finite-horizon H_∞ consensus control problem is studied for multi-agent systems under the limited energy constraint. Due to the limited energy, only a part of agents can use high energy to transmit information infallibly, and the remaining agents are randomly allocated low energy with several levels, which may lead to packet loss in some sense. Different levels result in different packet dropout probability. The purpose of this paper is to design a probability-dependent controller such that, for all probabilistic energy allocation and packet dropout, the H_∞ consensus performance can be guaranteed for multi-agent systems over a finite horizon. To this end, a stochastic and high-availability energy allocation method is first presented via stratified multi-objective optimization methods and stochastic analysis methods. Based on this novel allocation, a H_∞ consensus controller depending on the varying energy allocation is established. Furthermore, in terms of the probability information of both energy allocation and packet dropout, important results are obtained to guarantee the desired performance of the designed probability-dependent controller, and the controller are explicitly parameterized by means of the solutions to a set of linear matrix inequalities. Finally, a simulation example is utilized to illustrate the usefulness of the proposed controller design method.     

Strong γc-γcl H∞ stabilization for networked control systems under denial of service attacks

This paper is concerned with the strong γ_c-γ_cl H_∞ stabilization problem for networked control systems (NCSs) subject to denial of service (DoS) attacks, which are common attack behaviors that affect the packet transmission of measurement or control signals. The purpose of the problem under consideration is to design a stable dynamic output feedback (DOF) controller (strong stabilizing controller) with the prescribed H_∞ performance norm bound γ_c to tolerate multiple packet dropouts caused by DoS attacks, such that, the closed-loop system is mean-square stable and captures the H_∞ disturbance attenuation norm bound γ_cl. Based on the Lyapunov functional and the stochastic control approach, some sufficient conditions with the form of matrix inequalities for the existence of the desired stable DOF controller are established. Then, by an orthogonal complement space technique, the controller gain is parameterized. Next, an iterative linear matrix inequality (LMI) algorithm is developed to obtain the controller gain. Finally, the usefulness of the proposed method is indicated by a numerical simulation example.     

Observer-based control for singular nonhomogeneous Markov jump systems with packet losses

This paper is concerned with the observer-based H_∞ control for a class of singular Markov jump systems over a finite-time interval, where the transition probability (TP) is time-varying and is limited to a convex hull. Due to the limited capacity of network medium, packet losses are presented in the underlying systems. Firstly, using a stochastic Lyapunov functional, a sufficient condition on singular stochastic H_∞ finite-time boundedness for the corresponding closed-loop error systems is provided. Subsequently, a linear matrix inequality (LMI) condition on the existence of the H_∞ observer-based controller is developed from a new perspective. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed controller design method, wherein it is shown that the proposed method yields less conservative results than those in the literature.     

Event-based dynamic output-feedback controller design for networked control systems with sensor and actuator saturations

This paper is concerned with the problem of event-triggered dynamic output-feedback H_∞ control for networked control system with sensor and actuator saturations. The event-triggered scheme combined with sensor saturation is first introduced to judge whether the newly sampled signal should be transmitted to the dynamic output-feedback controller or not. Under this scheme, the concurrent closed-loop system is first modeled as a control system with an interval time-varying delay and nonlinear items. Through constructing the Lyapunov–Krasovskii functional and employing linear matrix inequality approach, sufficient conditions for H_∞ asymptotical stability are derived for the networked control system; furthermore, under the above stability condition, a dynamic output-feedback controller and the corresponding event-triggered parameters are co-designed through linear matrix inequality approach. Lastly, a numerical example is employed to prove the practical utility of this method.     

Resilient control based on disturbance observer for nonlinear singular stochastic hybrid system with partly unknown Markovian jump parameters

In this paper, the composite anti-disturbance resilient control is considered for nonlinear singular stochastic hybrid system with partly unknown Markovian jump parameters under multiple disturbances. Three kinds of disturbances are included in the studied system. One is generated by an external system and it enters the hybrid system from the channel of the control input. The other one is stochastic white noise. And the third one is the external unknown time-varying disturbance and it is supposed to be H₂ norm bounded. By combining the disturbance-observer-based-control scheme, H_∞ control technique and resilient control method, a composite anti-disturbance resilient controller is constructed to attenuate and eliminate the affection of these disturbances, and ensures the whole closed-loop system regular, impulse free and stochastically stable with the corresponding control performance. Then, some sufficient conditions and the gains of the controller and observer are obtained by using Lyapunov function method and the linear matrix inequalities (LMIs) technique. Finally, two numerical examples are given to show the effectiveness of presented method.     

Robust state-feedback control design for active suspension system with time-varying input delay and wheelbase preview information

This paper develops a robust state-feedback controller for active suspension system with time-varying input delay and wheelbase preview information in the presence of the parameter uncertainties. By employing system augmentation technique, a multi-objective control optimization model is first established and then this controller design is converted to a static full-state feedback controller design with robust H_∞ and generalized H₂ performance, wherein the model-dependent control gain is evaluated by transforming the related nonlinear matrix inequalities into their corresponding linear matrix inequality forms based on Lyapunov theory, and then LMI (Linear-Matrix-Inequality) technique is applied to solve and obtain the desired controller. A numerical simulation case is finally provided to reveal the effectiveness and advantages of the proposed controller.     

A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

In this paper, a sliding-mode approach is proposed for exponential H_∞ synchronization problem of a class of master–slave time-delay systems with both discrete and distributed time-delays, norm-bounded nonlinear uncertainties and Markovian switching parameters. Using an appropriate Lyapunov–Krasovskii functional, some delay-dependent sufficient conditions and a synchronization law, which include the master–slave parameters are established for designing a delay-dependent mode-dependent sliding mode exponential H_∞ synchronization control law in terms of linear matrix inequalities. The controller guarantees the H_∞ synchronization of the two coupled master and slave systems regardless of their initial states. Two numerical examples are given to show the effectiveness of the method.     

Robust mixed H2/H∞ model predictive control for Markov jump systems with partially uncertain transition probabilities

This paper addresses the control problem for a class of discrete-time Markov jump linear systems with partially unknown transition probabilities using model predictive controller subject to external disturbances and input constraints. Our focus is on the design of a model predictive controller to stabilize the system with a given mixed H₂/H_∞ performance index. Sufficient conditions are derived in terms of a set of linear matrix inequalities. Examples are presented to demonstrate the effectiveness of the proposed controller design method.     

Stability, L1-gain analysis and asynchronous L1-gain control of uncertain discrete-time switched positive linear systems with dwell time

In this paper, the stability, L₁-gain analysis and asynchronous L₁-gain control problems of uncertain discrete-time switched positive linear systems (DSPLSs) with dwell time are investigated. First, several convex and non-convex conditions on dwell time stability of DSPLSs with interval and polytopic uncertainties are presented, and the relation between these conditions is revealed. Then, via a switched dwell-time-dependent co-positive Lyapunov functions (SDTLFs) approach, convex sufficient conditions on L₁-gain analysis and asynchronous L₁-gain control of DSPLSs with interval uncertainties are derived. Meanwhile, via the switched parameter-dwell-time-dependent co-positive Lyapunov functions (SPDTLFs) approach, the L₁-gain analysis and asynchronous L₁-gain controller design problems of DSPLSs with polytopic uncertainties are also solved. The stability and L₁-gain analysis results are given in terms of linear programming (LP). The controller design results are presented in terms of bilinear programming (BP), which can be solved with the help of iterative algorithm. At last, both numerical and practical examples are provided to show the effectiveness of the results.     

H∞ finite-time control for LPV systems with parameter-varying time delays and external disturbance via observer-based state feedback

This paper is concerned with the observer-based H_∞ finite-time control problem for linear parameter-varying (LPV) systems with parameter-varying time delays and external disturbance. The main contribution is to design an observer-based H_∞ finite-time controller such that the resulting closed-loop system is uniformly finite-time bounded and satisfies a prescribed H_∞ disturbance attenuation level in a finite-time interval. By using the delay- and parameter-dependent multiple Lyapunov–Krasovskii functional approach, sufficient criteria on uniform H_∞ finite-time stabilization via observer-based state feedback are presented for the solvability of the problem, which can be tackled by a feasibility problem in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the validity of the proposed theoretical results.     

A state estimation H∞ issue for discrete-time stochastic impulsive genetic regulatory networks in the presence of leakage,multiple delays and Markovian jumping parameters

In this work, we probes the stability results of H_∞ state estimation for discrete-time stochastic genetic regulatory networks with leakage, distributed delays, Markovian jumping parameters and impulsive effects. Here, we focus to evaluate the true absorption of mRNAs and proteins by calculating the H_∞ estimator in such a way that the estimation error dynamics is stochastically stable during the completion of the prescribed H_∞ disturbance attenuation level. In favor of decreasing the data communion in trouble, the H_∞ system accept and evaluate the outputs that are only transferred to the estimator when a certain case is acroses. Further, few sufficient conditions are formulated, by utilizing the Lyapunov–Krasovskii functional under which the estimation error system is stochastically stable and also satisfied the H_∞ attainment constraint. The estimator is obtained in terms of linear matrix inequalities (LMIs) and these LMIs are attainable, only if the estimator gains can be absolutely given. In addition to that, two numerical examples are exposed to establish the efficiency of our obtained results.     

Finite-time H∞ control for a class of discrete-time nonlinear singular systems

This paper investigates the finite-time control problems for a class of discrete-time nonlinear singular systems via state undecomposed method. Firstly, the finite-time stabilization problem is discussed for the system under state feedback, and a finite-time stabilization controller is obtained. Then, based on which, the finite-time H_∞ boundedness problem is studied for the system with exogenous disturbances. Finally, an example of population distribution model is presented to illustrate the validity of the proposed controller. Because there is no any constraint for singular matrix E in the paper, controllers can be designed for more discrete-time nonlinear singular systems.     

A trust-region method for H2 model reduction of bilinear systems on the Stiefel manifold

This paper investigates the Riemannian trust-region method for H₂ model reduction of bilinear systems. The H₂ error norm is treated as a cost function on the Stiefel manifold such that the orthogonality constraint for the projection matrix is plainly satisfied. The property related to the Euclidean gradient is studied. Then, the inner product associated with the Riemannian Hessian is derived, which can simplify the expression of the trust-region subproblem. The trust-region method for H₂ model reduction is accordingly established and the convergence is further discussed. Finally, two numerical examples are employed to demonstrate the performance of the proposed method.     

l1 filtering for continuous-discrete T-S fuzzy positive Roesser model

This paper addresses the positive filter design problem for a class of continuous-discrete Roesser model in Takagi-Sugeno fuzzy form. Both the observer-based and the general form of filters are designed with l₁ performance constraint. By utilizing the co-positive Lyapunov function approach, sufficient criteria are derived in the form of linear programming, which not only guarantee the existence of the positive lower-bounding/upper-bounding filters but also assure the resulting filtering error system to be asymptotically stable and having a prescribed l₁-gain performance index. In addition, the explicit design schemes for the corresponding filter parameters are also presented. Finally, two numerical examples are provided to illustrate effectiveness of the proposed results.     

Output feedback robust H∞ control for spacecraft rendezvous system subject to input saturation: A gain scheduled approach

In this paper, the problem of output feedback robust H_∞ control for spacecraft rendezvous system with parameter uncertainties, disturbances and input saturation is investigated. Firstly, a full-order state observer is designed to reconstruct the full state information, whose gain matrix can be obtained by solving the linear matrix inequality (LMI). Subsequently, by combining the parametric Riccati equation approach and gain scheduled technique, an observer-based robust output feedback gain scheduled control scheme is proposed, which can make full use of the limited control capacity and improve the control performance by scheduling the control gain parameter increasingly. Rigorous stability analyses are shown that the designed discrete gain scheduled controller has faster convergence performance and better robustness than static gain controller. Finally, the performance and advantage of the proposed gain scheduled control scheme are demonstrated by numerical simulation.     

Reliable H∞ control on saturated linear Markov jump system with uncertain transition rates and asynchronous jumped actuator failure

This paper is concerned with reliable H_∞?control for saturated linear Markov jump systems with uncertain transition rates and asynchronous jumped actuator failure. The actuator failures are assumed to occur randomly under the Markov process with a different jumping mode from the system jumping mode. In considering the mixed-mode-dependent state feedback controller, both H_∞ stochastic stability analysis for closed-loop system with completely accessible transition rates and uncertain transition rates are investigated. Moreover, based on the obtained stability conditions, the H_∞?control problems are investigated, and the controller gains can be obtained by solving a convex optimization problem with minimizing H_∞ performance as objective and linear matrix inequalities (LMIs) as constraints. The problem of designing state feedback controllers such that the estimate of the domain of attraction is enlarged is also formulated and solved as an optimization problem with LMI constraints. Simulation results are presented to illustrate the effectiveness of the proposed results.     

Mixed H∞ and passivity control for a class of stochastic nonlinear sampled-data systems

In this paper, we consider the problem of mixed H_∞ and passivity control for a class of stochastic nonlinear systems with aperiodic sampling. The system states are unavailable and the measurement is corrupted by noise. We introduce an impulsive observer-based controller, which makes the closed-loop system a stochastic hybrid system that consists of a stochastic nonlinear system and a stochastic impulsive differential system. A time-varying Lyapunov function approach is presented to determine the asymptotic stability of the corresponding closed-loop system in mean-square sense, and simultaneously guarantee a prescribed mixed H_∞ and passivity performance. Further, by using matrix transformation techniques, we show that the desired controller parameters can be obtained by solving a convex optimization problem involving linear matrix inequalities (LMIs). Finally, the effectiveness and applicability of the proposed method in practical systems are demonstrated by the simulation studies of a Chua’s circuit and a single-link flexible joint robot.     

Robust H∞ control of an observer-based repetitive-control system

This paper concerns the problem of designing a robust observer-based modified repetitive-control system with a prescribed H_∞ disturbance rejection level for a class of strictly proper linear plants with unknown aperiodic disturbances and time-varying structural uncertainties. A correction to the amount of the delay in the repetitive controller is introduced that leads to a significant improvement in tracking performance. An integrated performance index is defined to quantify the overall effect of rejecting the aperiodic disturbances and tracking the periodic reference input. A Lyapunov functional with two tuning parameters is used to derive a linear-matrix-inequality based robust stability condition for the system with a prescribed disturbance-rejection bound. Combining the performance indices, an optimization algorithm that searches for the best combination of state-observer gain and the feedback control gains is developed. A numerical example illustrates the design procedure and demonstrates the effectiveness of the method.     

An improved memory-event-triggered control for networked control systems

In this paper, the H_∞ control problem is investigated for a class of networked control systems with network-induced delay. A memory event-triggered scheme (METS) is proposed to reduce the redundant packet transmission in the network channel. Different from the normal event-triggered scheme (ETS), some recent released packets are stored at the event generator and controller sides, which are utilized for the first time to generate the triggered events and design the memory-based controller. The proposed METS has the following two merits. (1) The information of certain recent released signals are first utilized, which helps to improve the triggering instants at the crest or trough of the responses. (2) A state-dependent time-varying threshold parameter is designed, which can adjust the packet transmission rate according to the information of the state. Based on the proposed METS, a memory event-triggered controller is designed, the controller feedback gains and triggering parameters can be co-designed by solving a set of linear matrix inequalities. Finally, an example is given to illustrate the effectiveness of the proposed method.