Resilient dissipative dynamic output feedback control for uncertain Markov jump Lur’e systems with time-varying delays

The resilient dissipative dynamic output feedback control problem for a class of uncertain Markov jump Lur’e systems with piecewise homogeneous transition probabilities and time-varying delays in the discrete-time domain are examined in this study. The designed controller can tolerate additive uncertainties in the controller gain matrix, which result from controller implementations. The time-varying delays are also supposed to be mode-dependent with lower and upper bounds known a priori. By constructing a Lyapunov–Krasovskii functional candidate, the sufficient conditions regarding the existence of desired resilient dissipative controllers are obtained in terms of linear matrix inequalities, thereby ensuring that the resulting closed-loop system is stochastically stable and strictly dissipative. Two numerical examples were established to illustrate the effectiveness of the proposed theoretical results.     

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In this paper, we extend the previous Markov-modulated reflected Brownian motion model discussed in [1] to a Markov-modulated reflected jump diffusion process, where the jump component is described as a Markov-modulated compound Poisson process. We compute the joint stationary distribution of the bivariate Markov jump process. An abstract example with two states is given to illustrate how the stationary equation described as a system of ordinary integro-differential equations is solved by choosing appropriate boundary conditions. As a special case, we also give the sationary distribution for this Markov jump process but without Markovian regime-switching.     

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In this paper, the asymptotic behavior of the weak solution (u_t)_{t\ge0} to the non-local Cauchy problems as stated in (1) is considered. Only using lower bounds of jumping kernel J(x,y) for large |x-y|, it is obtained that \|u_t\|_p\le c(t)\|u_0\|_q with any 1\le q相似文献   

Existence and uniqueness of perturbed reflected jump diffusion processes

In this article, we establish the existence of the solution to the càdlàg perturbed Skorohod problem. As an application, we obtain the existence and uniqueness of the solution to the perturbed reflected jump diffusion processes.     

Sudden Blocking of a Supercritical Open‐Channel Flow

This paper reports results of experiments in which a steadystate nonuniform supercritical openchannel flow was suddenly blocked by a rapidly falling gate at a downstream distance of about one hundred critical depths. This results in a hydraulic jump propagating upstream. Experimental data on the shape, height, and propagation speed of its leading front are given. It is shown that the parameters of the jump differ significantly from the values found using a quasistationary approach.     

Similarity Solutions for Thawing Processes with a Heat Flux Condition at the Fixed Boundary

Similarity solutions for a mathematical model for thawing in a saturated semi-infinite porous medium is considered when change of phase induces a density jump and a heat flux condition of the type is imposed on the fixed face x=0. Different cases depending on physical parameters are analysed and the explicit solution is obtained if and only if an inequality for the thermal coefficient q ₀ is verified. An improvement for the existence of a similarity solution for the same free boundary problem with a constant temperature on the fixed face x=0 is also obtained. Sommario. Vengono considerate soluzioni di similarità per un modello matematico di disgelo di un mezzo poroso saturo semi-infinito allorquando il cambiamento di fase induce un salto di densità ed una condizione di flusso di calore del tipo viene imposta sulla faccia fissa x=0. Si analizzano differenti casi dipendenti da parametri fisici e la soluzione esplicita viene ottenuta se e solo se risulta verificata una diseguaglianzo per il coefficiente termico q ₀. Si ottiene altresi un miglioramento della condizione di esistenza di una soluzione di similarità per lo stesso problema al contorno libero con temperatura costante sulla faccia fissa x=0.     

三维裂纹问题的高精度数值解法

提出了一种求解三维均质弹性体中任意形状平片裂纹问题超奇异积分方程组的Chebyshev多项式数值解法。数值计算结果表明：文中方法不仅收敛快，而且精度高。