This article investigates event-triggered and self-triggered $\mathcal {L}_{\infty }$ control problems for the Markov jump stochastic nonlinear systems subject to denial-of-service (DoS) attacks. When attacks prevent system devices from obtaining valid information over networks, a new switched model with unstable subsystems is constructed to characterize the effect of DoS attacks. On the basis of the switched model, a multiple Lyapunov function method is utilized and a set of sufficient conditions incorporating the event-triggering scheme (ETS) and restriction of DoS attacks are provided to preserve $\mathcal {L}_{\infty }$ performance. In particular, considering that ETS based on mathematical expectation is difficult to be implemented on a practical platform, a self-triggering scheme (STS) without mathematical expectation is presented. Meanwhile, to avoid the Zeno behavior resulted from general exogenous disturbance, a positive lower bound is fixed in STS in advance. In addition, the exponent parameters are designed in STS to reduce triggering frequency. Based on the STS, the mean-square asymptotical stability and almost sure exponential stability are both discussed when the system is in the absence of exogenous disturbance. Finally, two examples are given to substantiate the effectiveness of the proposed method.

In this article, the event-triggered resilient $\mathcal {L}_{\infty }$ control problem is concerned for the Markov jump systems in the presence of denial-of-service (DoS) jamming attacks. First, a fixed lower bound-based event-triggering scheme (ETS) is presented in order to avoid the Zeno problem caused by exogenous disturbance. Second, when DoS jamming attacks are involved, the transmitted data are blocked and the old control input is kept by using the zero-order holder (ZOH). On the basis of this process, the effect of DoS attacks on ETS is further discussed. Next, by utilizing the state-feedback controller and multiple Lyapunov functions method, some criteria incorporating the restriction of DoS jamming attacks are proposed to guarantee the $\mathcal {L}_{\infty }$ control performance of the event-triggered Markov closed-loop jump system. In particular, the bounded transition rates rather than the exact ones are taken into account. That is appropriate for the practical environment in which transition rates of the Markov process are difficult to measure accurately. Correspondingly, some criteria are proposed to obtain state-feedback gains and event-triggering parameters simultaneously. Finally, we provide two examples to show the effectiveness of the proposed method.

This paper applies a theoretical model developed recently to calculate the flow-instability inception of an axial transonic single stage compressor. After several calculation methods are compared, the singular value decomposition method is adopted to solve the resultant eigenvalue problem in which the involved matrix is rather large due to multistage configuration. The onset point of flow instability is judged by the imaginary part of the resultant eigenvalue. The effect of flow compressibility on the stall onset point calculation for the transonic rotor is studied. It is shown that the compressibility of flow perturbation plays a major role in computing high speed compressor flow stability.

An in-depth understanding of stall behavior is essential to improve the safe and stable operation of the pump turbine. In this research, the Detached Eddy Simulation (DES) is used to investigate the variation characteristics and propagation mechanism of the rotating stall of the hump instability region. The frequency characteristics and spatial intensity distribution of the stall cells are studied by adopting the proper orthogonal decomposition (POD) method. The results indicate that the energy loss at 0.80Q_DES and 0.75Q_DES is induced by the rotating stall with three cells that occur in the diffuser flow channel, and the corresponding high amplitude frequencies are St_0.0074 and St_0.0111, respectively. The effect of the stall cells is particularly severe near the hub. When the flow rate is further reduced to 0.68Q_DES, the three rotating stall cells develop into two symmetrically distributed stable stall cells with no definite characteristic frequencies, and the blocking phenomenon is concentrated near the shroud. With the stall cells losing their rotational characteristics, they have less impact on the flow field and contribute less energy. This paper also reveals that the energy loss in the diffuser contributes significantly to the hump formation on the performance curve.