scholarly journals Stability of Linear Continuous Singular and Discrete Descriptor Systems over Infinite and Finite Time Interval

10.5772/16225 ◽  
2011 ◽  
Author(s):  
Dragutin Lj. ◽  
Tamara Nestorovi
2015 ◽  
Vol 2015 ◽  
pp. 1-14
Author(s):  
Baoyan Zhu ◽  
Jingjun Zhang ◽  
Daqing Zhang ◽  
Aibin Liu

Delay-dependent finite-timeH∞controller design problems are investigated for a kind of nonlinear descriptor system via a T-S fuzzy model in this paper. The solvable conditions of finite-timeH∞controller are given to guarantee that the loop-closed system is impulse-free and finite-time bounded and holds theH∞performance to a prescribed disturbance attenuation levelγ. The method given is the ability to eliminate the impulsive behavior caused by descriptor systems in a finite-time interval, which confirms the existence and uniqueness of solutions in the interval. By constructing a nonsingular matrix, we overcome the difficulty that results in an infeasible linear matrix inequality (LMI). Using the FEASP solver and GEVP solver of the LMI toolbox, we perform simulations to validate the proposed methods for a nonlinear descriptor system via the T-S fuzzy model, which shows the application of the T-S fuzzy method in studying the finite-time control problem of a nonlinear system. Meanwhile the method was also applied to the biological economy system to eliminate impulsive behavior at the bifurcation value, stabilize the loop-closed system in a finite-time interval, and achieve aH∞performance level.


2004 ◽  
Vol 41 (2) ◽  
pp. 570-578 ◽  
Author(s):  
Zvetan G. Ignatov ◽  
Vladimir K. Kaishev

An explicit formula for the probability of nonruin of an insurance company in a finite time interval is derived, assuming Poisson claim arrivals, any continuous joint distribution of the claim amounts and any nonnegative, increasing real function representing its premium income. The formula is compact and expresses the nonruin probability in terms of Appell polynomials. An example, illustrating its numerical convenience, is also given in the case of inverted Dirichlet-distributed claims and a linearly increasing premium-income function.


2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Li Liang

This paper is concerned with the problem of finite-time boundedness for a class of delayed Markovian jumping neural networks with partly unknown transition probabilities. By introducing the appropriate stochastic Lyapunov-Krasovskii functional and the concept of stochastically finite-time stochastic boundedness for Markovian jumping neural networks, a new method is proposed to guarantee that the state trajectory remains in a bounded region of the state space over a prespecified finite-time interval. Finally, numerical examples are given to illustrate the effectiveness and reduced conservativeness of the proposed results.


2011 ◽  
Vol 34 (7) ◽  
pp. 841-849 ◽  
Author(s):  
Shuping He ◽  
Fei Liu

In this paper we study the robust control problems with respect to the finite-time interval of uncertain non-linear Markov jump systems. By means of Takagi–Sugeno fuzzy models, the overall closed-loop fuzzy dynamics are constructed through selected membership functions. By using the stochastic Lyapunov–Krasovskii functional approach, a sufficient condition is firstly established on the stochastic robust finite-time stabilization. Then, in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of the stochastic finite-time controller are presented and proved. Finally, the design problem is formulated as an optimization one. The simulation results illustrate the effectiveness of the proposed approaches.


Optik ◽  
2019 ◽  
Vol 181 ◽  
pp. 404-407 ◽  
Author(s):  
Fatemeh Ahmadinouri ◽  
Mehdi Hosseini ◽  
Farrokh Sarreshtedari

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