Comments on "Sufficient conditions for stability of multidimensional discrete systems"

1985 ◽  
Vol 73 (4) ◽  
pp. 838-840 ◽  
Author(s):  
D.R. Reddy ◽  
R. Unbehauen ◽  
D. Hertz ◽  
E. Zeheb
Keyword(s):  
Sufficient Conditions ◽  
Discrete Systems ◽  
Multidimensional Discrete Systems

Stability and Stabilization for Discrete System With Probabilistic Nonlinearities

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Xia Zhao ◽  
Engang Tian
Keyword(s):  
Sufficient Conditions ◽  
Discrete Systems ◽  
System Model ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Mean Square Stability ◽  
New Type ◽  
Stability And Stabilization ◽  
The Mean ◽  
Varying Delay

This paper investigates stability and stabilization of discrete systems with probabilistic nonlinearities and time-varying delay. New characters of the nonlinearities, the probability of the nonlinearities happening between different bounds, are used to build new type of system model, which can help us make a full use of the inner variation information of the nonlinearities. With the help of the new characters, new system model is proposed. Then, sufficient conditions for the mean square stability of the system can be obtained by using the Lyapunov functional approach and linear matrix inequalities technique. An example is proposed to illustrate the efficiency of the proposed method.

scholarly journals An Approach for Solving Discrete Game Problems with Total Constraints on Controls

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Asqar Raxmonov ◽  
Gafurjan I. Ibragimov
Keyword(s):  
Explicit Form ◽  
Control Parameter ◽  
Sufficient Conditions ◽  
Discrete Systems ◽  
Nonempty Interior ◽  
Pursuit Game ◽  
Terminal Set ◽  
Control Forces ◽  
Linear Discrete Systems ◽  
Discrete Game

We consider a linear pursuit game of one pursuer and one evader whose motions are described by different-type linear discrete systems. Controls of the players satisfy total constraints. Terminal setMis a subset ofℝnand it is assumed to have nonempty interior. Game is said to be completed ifyk-xk∈Mat some stepk. To construct the control of the pursuer, at each stepi, we use positions of the players from step 1 to stepiand the value of the control parameter of the evader at the stepi. We give sufficient conditions of completion of pursuit and construct the control for the pursuer in explicit form. This control forces the evader to expend some amount of his resources on a period consisting of finite steps. As a result, after several such periods the evader exhausted his energy and then pursuit will be completed.

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