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.     

Robust H∞ control for a class of uncertain nonlinear systems with mixed time-delays

This paper is concerned with the robust H_∞ control problem for a general class of uncertain nonlinear systems with mixed time-delays. The mixed time-delays consist of both discrete and distributed delays. We aim to design a memoryless state feedback controller such that the closed-loop system is robustly stable for all admissible uncertainties with guaranteed H_∞ disturbance rejection attenuation level. By introducing a new Lyapunov–Krasovskii functional that reflects the mixed delays, sufficient conditions are established for the closed-loop system ensuring the robust stability as well as the H_∞ performance requirement. The controller design is facilitated in terms of the solvability of a Hamilton–Jacobi inequality. Two numerical examples are utilized to demonstrate the effectiveness of the proposed methods.     

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.     

H∞ tracking control for a class of asynchronous switched nonlinear systems with uncertain input delay

This paper studies the problems of stability and H∞ model reference tracking performance for a class of asynchronous switched nonlinear systems with uncertain input delay. First, it is assumed switched controller and corresponding piecewise Lyapunov function are unknown but the derivative of piecewise Lyapunov function has a condition; this condition implies that the nominal system (system without input delay and disturbance) is exponentially stable by any switched controller which satisfies this condition. With this assumption, a proper Lyapunov–Krasovskii functional is constructed. By employing this new functional and average dwell time technique, the delay-dependent input-to-state stability criteria are derived under a certain delay bound; in addition, a mechanism which finds the upper bound of input delay is proposed. Finally, a kind of state feedback control law which fulfils condition of aforesaid piecewise Lyapunov function is introduced to guarantee the input-to-state stability and H∞ model reference tracking performance. Simulation examples are presented to demonstrate the efficacy of results.     

Event-triggered ε level H∞ probabilistic control of uncertain systems

In this paper, a new event-trigger based probabilistic controller is designed using a scenario optimization approach for the robust stabilization of uncertain systems subject to nonlinear and unbounded uncertainties. Sufficient probabilistic stabilization conditions are derived under which the closed-loop system is ε level robust probabilistic stable. Based on these conditions, the design of the gains of the event-triggered state feedback controller is formulated and solved as an optimization problem involving linear matrix inequality. The applicability of theoretical results obtained is illustrated by a numerical example.     

Event-triggered H∞ filtering control for a class of distributed parameter systems with Markovian switching topology

The H_∞ filtering problem for distributed parameter systems with stochastic switching topology is investigated in this paper based on event-triggered control scheme. The switching topology which subjects to a Markovian chain is considered in filter design because of the communication uncertainty of practical networks. An event-triggered mechanism as a sampling scheme is developed aiming at the benefit of reducing the computation load or saving the limited network resources. Based on some novel integral inequalities, the improved delayed method is proposed for the H_∞ filtering control problem with event-triggered scheme. Moreover, by employing stochastic stability theory, filters with Markovian jump parameters are designed to guarantee that the stochastically mean square stability and H_∞ performance of the underlying error system. Finally, in order to illustrate the applicability of the obtained results, numerical examples are presented.     

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.     

Backstepping-based decentralized bounded-H∞ adaptive neural control for a class of large-scale stochastic nonlinear systems

In this paper, a novel decentralized adaptive neural control approach based on the backstepping technique is proposed to design a decentralized H_∞ adaptive neural controller for a class of stochastic large-scale nonlinear systems with external disturbances and unknown nonlinear functions. RBF neural networks are utilized to approximate the packaged unknown nonlinearities. A novel concept with regard to bounded-H_∞ performance is proposed. It can be applied to solve an H_∞ control problem for a class of stochastic nonlinear systems. The constant terms appeared in stability analysis are dealt with by using Gronwall inequality, so that H_∞ performance criterion is satisfied. The assumption that the approximation errors of neural networks must be square-integrable in some literature can be eliminated. The design process for decentralized bounded-H_∞ controllers is given. The proposed control scheme guarantees that all the signals in the resulting closed-loop large-scale system are uniformly ultimately bounded in probability, and each subsystem possesses disturbance attenuation performance for external disturbances. Finally, the simulation results are provided to illustrate the effectiveness and feasibility of the proposed approach.     

Standard H∞ performance of switched delay systems under minimum dwell time switching

This paper investigates the standard H_∞ performance for a class of switched linear systems with time-varying delay in the framework of the delay-dependent/delay-independent minimum dwell time. For the studied systems, we first construct two types of multiple time-varying Lyapunov functionals, and then obtain the sufficient conditions by restricting the decay of the Lyapunov functional of the active subsystem and forcing “energy” of the overall switched system to decrease at switching instants by the proposed Lyapunov functionals to guarantee standard L₂-gain performance meanwhile ensuring their internal stability with minimum dwell time switching. Finally, two examples are presented to illustrate the effectiveness of the proposed results.     

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-time analysis and H∞ control for switched stochastic systems

This paper is concerned with the finite-time stability, boundedness and H_∞ control problems for a class of switched stochastic systems. Using the average dwell time method and the multiple Lyapunov-like function technique, some sufficient conditions are proposed to guarantee the finite-time properties for the switched stochastic systems in the form of matrix inequalities. Also, a state feedback controller for the finite-time H_∞ control problem is obtained. An example is employed to verify the effectiveness of the proposed method.     

Robust H∞ filtering for switched stochastic systems under asynchronous switching

This paper investigates the problem of robust H_∞ filtering for switched stochastic systems under asynchronous switching. The so-called asynchronous switching means that the switching between the filters and system modes is asynchronous. The aim is to design a filter ensuring robust exponential mean square stability and a prescribed H_∞ performance level for the filtering error systems. Based on the average dwell time approach and piecewise Lyapunov functional technique, sufficient conditions for the existence of the robust H_∞ filter are derived, and the proposed filter can be obtained by solving a set of LMIs(linear matrix inequalities). Finally, a numerical example is given to show the effectiveness of the proposed approach.