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In this paper, the event-triggered stochastic consensus for networked Lagrangian systems with semi-Markov switching topologies and communication delays is considered. An event-triggered sampling control strategy is used to design the distributed stochastic consensus scheme of networked Lagrangian systems for two cases with leader and leaderless. Two delay-dependent consensus criteria are derived in the sense of mean square by use of a suitable Lyapunov-Krasovskii functional and the stochastic delayed Halanay inequality, respectively. A key feature of the developed event-triggered consensus algorithm is to introduce a suitable adjustment parameter on consensus control gains characterizing the effect of both semi-Markov switching topology and communication delay. Finally, a numerical example of four manipulators with two links is presented to illustrate the effectiveness of the developed event-triggered methodology.

This paper addresses the problem of event-triggered dynamic output feedback control for uncertain Markovian jump systems with partly unknown transition rates. An event-triggered dynamic output feedback control scheme is proposed to stabilize a class of uncertain networked Markovian jump systems with partly unknown transition rates, and a suitable Lyapunov–Krasovskii functional is then introduced to guarantee the asymptotical stability in mean-square sense of the closed-loop controlled system. It is shown that the proposed control scheme is relatively convenient to choose the control gain matrices by the use of the Matlab LMIs Toolbox, and thus it might be convenient to application in practice. Finally, numerical examples are presented to illustrate the effectiveness of the proposed methodology.

This paper is concerned with the problem of fault detection filtering for a class of nonhomogeneous Markov jump systems with randomly occurring sensor saturations, where it is assumed that sensor saturation is randomly occur satisfying the Bernoulli distribution, meanwhile transition probabilities in nonhomogeneous Markov chain are time-varying. By employing the suitable Lyapunov technique in combination with Linear Matrix Inequalities (LMIs), some sufficient criteria are derived to guarantee that the augmented system is mean square stochastically stable with an H∞ performance level. Finally, a representative example of industrial stirred tank reactor systems is presented to illustrate the theoretical results, and it then turns out that the feasible filtering parameters can be exactly fixed by Matlab Tool Box, and the H∞ performance of the system can be fully guaranteed by the proposed control strategy.

The problem of distributed event-triggered mean square consensus for networked Lagrangian systems with communication delays and semi-Markov switching topologies is considered in this brief. By considering event-triggered sampling control with stochastic disturbances, the distributed stochastic consensus protocol is proposed. Furthermore, by using stochastic analysis theory, with a combination of both algebraic graph tools and linear matrices inequalities (LMIs), a general delay-dependent criterion is presented for solving stochastic consensus problems in terms of mean square under the semi-Markov switching network topology structure with communication delays. Meanwhile, Zeno behavior of the triggering time sequences is also avoided. Subsequently, a typical example of four manipulators with two links is provided to demonstrate the developed consensus methodology in this brief.

In this brief, the problem of $H_{\infty}$ output feedback control for a class of continuous time singular Markovian jump systems with unknown transition rates is addressed, and here the transition rates are assumed to be unknown but have the upper bound and the low bound. By employing a suitable Lyapunov functional in combination with the infinitesimal operator, some simple yet general conditions in terms of linear matrix inequalities (LMIs) are proposed to guarantee that such a class of continuous time singular Markovian jump systems is stochastically admissible, and has a prescribed level of $H_{\infty}$ performance. To this end, a typical numerical example and its simulations are implemented by Matlab LMI Toolbox to demonstrate the effectiveness of the proposed control methodology.

The regeneration of injured spinal cord in applied weak DC electrical field has been demonstrated for years. However, the most suitable stimulating intensity has not been confirmed because the mechanism of axonal regeneration in applied DC electrical field is absent. This paper used finite element method to analyze the distribution of electrical field before and after injury and the uniformity of electrical field induced by different number of stimulating electrodes. Moreover, we improved the implantable oscillating field stimulator (OFS) to make it more reliable, effective and steady. In animal experiment, voltages between stimulating electrodes have been successfully recorded in different conditions such as intact, injured, exposing spinal column and suturing skin. Simulation results showed that the uniformity of electrical field of three pairs of electrodes is better than that of one pair. Experimental results indicated that a stimulating current of 10µA could generate an approximate 500µV/mm electrical field on the exposed spinal cord of rat, but a lower electrical field after suturing. In addition, voltages between stimulating electrodes would increase in deed because of transection of spinal cord.