The asynchronous sliding mode control (SMC) problem is investigated for networked Markovian jump Lur’e systems, in which the information of system modes is unavailable to the sliding mode controller but could be estimated by a mode detector via a hidden Markov model (HMM). In order to mitigate the burden of data communication, an event-triggered protocol is proposed to determine whether the system state should be released to the controller at certain time-point according to a specific triggering condition. By constructing a novel common sliding surface, this paper designs an event-triggered asynchronous SMC law, which just depends on the hidden mode information. A combination of the stochastic Lur’e-type Lyapunov functional and the HMM approach is exploited to establish the sufficient conditions of the mean square stability with a prescribed ${H}_{\infty }$ performance and the reachability of a sliding region around the specified sliding surface. Moreover, the solving algorithm for the control gain matrices is given via a convex optimization problem. Finally, an example from the dc motor device system is provided.

An Event-Triggered Approach to Sliding Mode Control of Markovian Jump Lur’e Systems Under Hidden Mode Detections

In this paper, we consider the distributed filtering problem for continuous-time stochastic systems over sensor networks subject to Markovian switching topologies. Due to limited communication energy and bandwidth, an event-based communication scheme is proposed with the aim to decrease the transmission frequency. An individual triggering condition is put forward to regulate the communication rates for each component of the system state in order to better reflect the engineering requirements. The aim of this paper is to design a distributed filter over sensor networks with Markovian switching topologies such that the dynamics of the estimation error is exponentially mean-square bounded. It is shown that, with the proposed event-based distributed filtering algorithm, the exponential mean-square boundedness of the estimation errors is guaranteed if the sensor network is distributively detectable and the combined communication topology is strongly connected. A numerical example is presented to illustrate the usefulness of the developed algorithm.

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Event-Based Distributed Filtering Over Markovian Switching Topologies

Monotone dynamical systems Stability and convergence Competitive and cooperative differential equations Irreducible cooperative systems Cooperative systems of delay differential equations Nonquasimonotone delay differential equations Quasimonotone systems of parabolic equations A competition model Appendix Bibliography.

Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith

This paper addresses the problem of reachable set estimation for a class of Takagi-Sugeno fuzzy model based Markov jump inertial neural networks with time-varying delay. The objective of this paper is to obtain a compact set bounding all states of the system from some domains under initial conditions, while all the states from other domain are exponential convergence in another compact set. Primarily, on the basis of the Lyapunov-Krasovskii functional (LKF), in which both the upper and lower bounds of time-varying delay as well as the triple-summation term are considered, a novel approach of combining the reciprocally convex combination and weighted summation inequalities is employed to get the less conservative conditions. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.

Fanwei Meng

Papers

New criteria for exponential stability of switched time-varying systems with delays and nonlinear disturbances

State bounding for switched homogeneous positive nonlinear systems with exogenous input