Event-triggered H∞ output feedback control for discrete Markov jump systems with quantizations

This paper presents a novel event-triggered communication scheme for sample-data systems. Firstly, a novel event-triggered communication scheme for sample-data systems is proposed, which can reduce the data communication. Secondly, a model of the considered system is built under consideration of the event-triggered communication scheme. Then, the H ∞ performance analysis and H i controller design conditions for the studied system are obtained. Finally, an example shows that the effectiveness of the developed method.

This article focuses on the event-triggered <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H\infty$</tex-math></inline-formula> control problem of the networked descriptor system with time delays. First, a novel event-triggered communication strategy is proposed, which can adaptively adjust the triggering parameters in light of dynamic errors. The expected control performance can be ensured in parallel with saving limited communication resources. Second, an integrated system model is established by considering network-induced delays, event-triggered strategy, and systems' time-varying delays. A co-design control method based on the event-triggered strategy is proposed by implementing the Lyapunov method. Finally, the effectiveness and advantages of the proposed method are presented through two examples.

PurposeThe purpose of this paper is to propose a decentralized output feedback controller for cooperative attitude regulation of spacecraft formation in absence of angular velocity feedback.Design/methodology/approachThe nonlinear relative attitude dynamic and kinematic equations represented by relative quaternion and relative angular velocity, respectively, are considered in this paper. The lead filter is employed to synthesize virtual angular velocity signal so that the design of output feedback controller is achieved. Lyapunov method is adopted to prove the stability of closed‐loop system. Considering the external disturbance, the theory of L2‐gain disturbance attenuation is employed to improve the designed controller. Numerical simulations are carried out to verify the controllers proposed.FindingsIt is found that the closed‐loop system can be guaranteed asymptotically stable in absence of external disturbance. When disturbance is considered, as long as the sufficient condition proposed is satisfied, the improved controller can render system uniformly ultimately bounded stable.Practical implicationsThe proposed output feedback control scheme can be considered as a fall‐back alternative for the case that the angular velocity sensors fail, or seen as another option for the system without angular velocity sensors at all.Originality/valueUnlike most classical works in the field of output feedback which focus on centralized scheme and neglect the disturbance, the controller proposed in this paper is able to handle the output feedback control problem of multi‐agent formation in a decentralized fashion, so as to avoid the single failure point of a centralized scheme. Meanwhile, the capability of L2‐gain disturbance attenuation is also achieved simultaneously.

This paper is concerned with the $$H_{\infty }$$ filtering problem for discrete-time Markov jump systems with repeated scalar nonlinearities in an event-triggered communication scheme. An event-triggered scheme is proposed to determine whether the current data should be transmitted to the filter or not. Based on the time interval analysis approach, the discrete-time Markov jump system with network-induced delays under event-triggered communication scheme is converted into the discrete-time Markov jump time-delay system. By employing the positive-definite diagonally-dominant-type Lyapunov function technique, criteria are derived to guarantee the system is stochastically stable with a prescribed $$H_{\infty }$$ performance level. The correspondent filter and the event-triggered parameters are also solved. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

This paper considers the development of dynamic output feedback H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controllers for a class of discrete-time Markov jump systems with the transition probability matrix partly unknown. Sufficient conditions are proposed to guarantee the stochastic stability of the underlying system through using several linear matrix inequations. The system is not only stabilization under the designed output feedback controller but also with a γ performance. Numberical examples are given to show the potential of the proposed techniques.

In this paper, we focus on the design of output feedback controller for a class of discrete-time nonlinear systems combined with event-triggered control approach. The designed event-triggered threshold is related to the output signal, which further reduces the tracking error. Besides, by co-designing backstepping control method and the event-triggered strategy, the corresponding assumptions for input-to-state stable (ISS) with respect to the measurement errors can be removed. The stability analysis result shows that all signals in the closed-loop system are bounded and the tracking error is bounded by a small constant depending on event-triggered threshold parameter. Simulation results show the performance and effectiveness of the designed controller.

Event-triggered controller design of nonlinear discrete-time networked control systems in T-S fuzzy model

A survey on recent advances in event-triggered communication and control

This paper is concerned with the output feedback control problem for a class of nonlinear system with time delay. First, a state feedback controller is design and a sufficient condition with exponential stability is obtained. Second, we study the observer design problem. And we proved that the observer designed in this paper ensure the observation error exponential converge to zero. Furthermore, output feedback controller using state feedback control and observer design is studied.

SummaryThis paper presents the design of output feedback controllers for discrete‐time (DT) linear systems. New sufficient LMI conditions are derived for designing static and controllers using decomposition of an auxiliary matrix. The decomposition facilitates linearization of nonlinear term of reduced size to obtain linear matrix inequality criteria. This leads to less conservative results as shown in the numerical examples. In addition, the proposed static output feedback criteria is also used for designing dynamic output feedback controllers for DT systems. Furthermore, a comparative study is also made for the proposed design method with the results existing in the literature. Finally, a DT static output feedback controller is designed for a quarter‐car suspension system. Simulation results are provided to show the efficacy of the proposed design method.

In this paper, for the purpose of improving the energy efficiency of the industrial sensor networks, we investigated the event-based H∞ filtering problem for a class of discrete-time nonlinear sensor network systems with time-varying delay, packet dropout, and multiplicative noises. Instead of traditional time-triggered communication mechanism, the event-triggered strategy is adopted in industrial sensor network, which could not only reduce the transmission frequency of the sensor measurement output, but also guarantee the prescribed filtering performance, if only the threshold in the event-triggered function is chosen suitably. The time-varying delay characteristic of systems is considered with the event-triggered strategy, which has seldom been studied due to the complexity of time-varying delay and event-triggered strategy. The most common network-induced phenomenon of packet dropout in industrial sensor network is described. The purpose is to design a filter satisfying exponentially stable and H∞ indexes. The main result is that sufficient conditions are established, guaranteeing our proposed filter satisfying filtering performance constraints, and the parameters of filter could be got through the derived linear matrix inequality (LMI), if only it is feasible. At last, the filtering approach is demonstrated by a simulation.

In this paper, finite-time contractive stability analysis and observer-based H ∞ fault tolerant control problem is discussed for a networked single-link flexible manipulator subject to external disturbance, actuator, and sensor faults. The variable delay is considered in both sensor-to-controller and controller-to-actuator channels. In order to conserve the network resources and avoid Zeno phenomenon, the sampled-data-based event-triggered scheme is employed, which only requires the system states in discrete instants. The nonlinear unknown input observer is first designed to achieve the estimation of the system states and faults simultaneously. To reduce the conservatism of designing procedure, the Lyapunov–Krasovskii functional approach is used, which includes the information of the lower and upper bounds of variable data transmission delay. Then, sufficient delay dependent conditions are derived and an observer-based feedback control law and observer gains are computed by a set of linear matrix inequalities to realize that the augmented system is finite-time contractive stable and the states of the system remain within a specified threshold during a fixed time interval, which is smaller than the initial state bound. Furthermore, the prescribed H ∞ performance is satisfied in the presence of external disturbance. At last, simulation results are given to confirm the validity of the presented approach.

This paper investigates the problem of event-triggered dynamic output feedback control for networked Takagi-Sugeno (T-S) fuzzy systems with asynchronous premise variables. Our attention is focused on the design of an event-triggered fuzzy dynamic output feedback controller that guarantees that the closed-loop system is asymptotically stable. First, with consideration of the limited bandwidth and restricted network resource, an event-triggered communication scheme is proposed to save the limited network resource. Second, different from the existing results in the literature, a fuzzy dynamic output feedback controller with asynchronous premise variables is constructed such that the premise membership functions are not necessarily the same as the networked T-S fuzzy systems. Then, by using the Wirtinger inequality and some slack matrices, a less conservative stability and stabilization conditions for the existence of fuzzy dynamic output feedback controller are derived in the form of linear matrix inequalities, which can be solved by the standard MATLAB toolbox. Finally, an example is given to demonstrate the effectiveness of the designed event-triggered fuzzy dynamic output feedback controller.

This paper deals with the problem of static output feedback (SOF) control design for a class of diffusion partial differential equation (PDE) and ordinary differential equation (ODE) cascades, where the ODE model is used to describe the dynamics of the multi-input and multi-output (MIMO) plant and the diffusion PDE model is employed to represent the dynamics of actuators. The objective of this paper is to develop a simple as well as effective SOF controller via the Lyapunov's direct method such that the resulting closed-loop system is globally exponentially stable. By constructing a quadratic Lyapunov function, the sufficient condition on the globally exponential stability of the closed-loop cascaded system is presented in terms of linear matrix inequality (LMI). Then, an LMI-based design method of the SOF controller is developed on the basis of the obtained stability analysis result. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method.

This paper is concerned with the issue of event-triggered sliding mode control for discrete-time Markov jump systems with partially unknown transition probabilities. The problems of information channel congestion are solved through the event-triggered scheme. By utilizing Lyapunov stability theory, sufficient conditions that ensure the sliding dynamics achieve the desired performance are derived. A new sliding mode control law is designed such that the reach ability, the stochastic stability and H α performance are guaranteed simultaneously. Finally, a numerical example is proposed to show the effectiveness of the sliding mode control scheme.