scholarly journals Finite-Time Stability Analysis of Discrete-Time Linear Singular Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Songlin Wo ◽  
Xiaoxin Han
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Singular Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Time Stability ◽  
Finite Time Stability ◽  
Necessary And Sufficient ◽  
Time Linear

The finite-time stability (FTS) problem of discrete-time linear singular systems (DTLSS) is considered in this paper. A necessary and sufficient condition for FTS is obtained, which can be expressed in terms of matrix inequalities. Then, another form of the necessary and sufficient condition for FTS is also given by using matrix-null space technology. In order to solve the stability problem expediently, a sufficient condition for FTS is given via linear matrix inequality (LMI) approach; this condition can be expressed in terms of LMIs. Finally, an illustrating example is also given to show the effectiveness of the proposed method.

Finite-Time Stability for Continuous-Time Linear Singular Systems

2013 ◽  
Vol 846-847 ◽  
pp. 383-387
Author(s):  
Song Lin Wo ◽  
Xiao Xin Han
Keyword(s):  
Continuous Time ◽  
Finite Time ◽  
Stability Problem ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Linear

In this paper the finite-time stability (FST) problem of continuous-time linear singular systems (CTLSS) is considered. The main results provided are a sufficient condition of FTS for CTLSS and a sufficient condition of robust FTS for uncertain CTLSS. Such sufficient conditions in the LMI formalism are attained for finite-time stability; this gives the opportunity of fitting the finite time stability problem in the general framework of the linear matrix inequality (LMI) approach. In this context an example is provided to demonstrate the application of the proposed method for CTLSS finite-time stability problem.

Admissible Finite-Time Stability and Stabilization of Uncertain Discrete Singular Systems

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Wenping Xue ◽  
Weijie Mao
Keyword(s):  
Finite Time ◽  
Controller Design ◽  
Singular Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Stability ◽  
Finite Time Stability ◽  
Fixed Parameter ◽  
Discrete Singular Systems ◽  
Definition Of

The problems of admissible finite-time stability (AFTS) and admissible finite-time stabilization for a class of uncertain discrete singular systems are addressed in this study. The definition of AFTS is first given. Second, a sufficient condition for the AFTS of the nominal unforced system is established, which is further extended to the uncertain case. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is admissibly finite-time stable for all admissible uncertainties. Both the AFTS and the controller design conditions are presented in terms of linear matrix inequalities (LMIs) with a fixed parameter. Finally, two numerical examples are provided to illustrate the effectiveness of the developed theory.

Positive Finite-Time Stabilization for Discrete-Time Linear Systems

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Wenping Xue ◽  
Kangji Li
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Initial State ◽  
Finite Time Stability ◽  
Time Linear

In this paper, a new finite-time stability (FTS) concept, which is defined as positive FTS (PFTS), is introduced into discrete-time linear systems. Differently from previous FTS-related papers, the initial state as well as the state trajectory is required to be in the non-negative orthant of the Euclidean space. Some test criteria are established for the PFTS of the unforced system. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is positively finite-time stable. This condition is provided in terms of a series of linear matrix inequalities (LMIs) with some equality constraints. Moreover, the requirement of non-negativity of the controller is considered. Finally, two examples are presented to illustrate the developed theory.

scholarly journals Controllability of Linear Discrete-Time Systems with Both Delayed States and Delayed Inputs

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Wenguang Luo
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Control Delay ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
And Control ◽  
Time Systems ◽  
Time Linear

The controllability issues for discrete-time linear systems with delay in state and control are addressed. By introducing a new concept, the controllability realization index (CRI), the characteristic of controllability is revealed. An easily testable necessary and sufficient condition for the controllability of discrete-time linear systems with state and control delay is established.

scholarly journals H_∞ Finite-time Boundedness for Discrete-time Delay Neural Networks via Reciprocally Convex Approach

2020 ◽  
Vol 36 (3) ◽  
Author(s):  
Le Anh Tuan
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Finite Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Discrete Time Delay ◽  
Finite Time Boundedness ◽  
Reciprocally Convex Approach

This paper addresses the problem of finite-time boundedness for discrete-time neural networks with interval-like time-varying delays. First, a delay-dependent finite-time boundedness criterion under the finite-time  performance index for the system is given based on constructing a set of adjusted Lyapunov–Krasovskii functionals and using reciprocally convex approach. Next, a sufficient condition is drawn directly which ensures the finite-time stability of the corresponding nominal system. Finally, numerical examples are provided to illustrate the validity and applicability of the presented conditions. Keywords: Discrete-time neural networks,  performance, finite-time stability, time-varying delay, linear matrix inequality.  

scholarly journals Finite-time Stability, Dissipativity and Passivity Analysis of Discrete-time Neural Networks Time-varying Delays

2019 ◽  
Vol 3 (6) ◽  
pp. 361-368
Author(s):  
Porpattama Hammachukiattikul
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Finite Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
The Neural Network ◽  
Network Time

The neural network time-varying delay was described as the dynamic properties of a neural cell, including neural functional and neural delay differential equations. The differential expression explains the derivative term of current and past state. The objective of this paper obtained the neural network time-varying delay. A delay-dependent condition is provided to ensure the considered discrete-time neural networks with time-varying delays to be finite-time stability, dissipativity, and passivity. This paper using a new Lyapunov-Krasovskii functional as well as the free-weighting matrix approach and a linear matrix inequality analysis (LMI) technique constructing to a novel sufficient criterion on finite-time stability, dissipativity, and passivity of the discrete-time neural networks with time-varying delays for improving. We propose sufficient conditions for discrete-time neural networks with time-varying delays. An effective LMI approach derives by base the appropriate type of Lyapunov functional. Finally, we present the effectiveness of novel criteria of finite-time stability, dissipativity, and passivity condition of discrete-time neural networks with time-varying delays in the form of linear matrix inequality (LMI).

scholarly journals Controllability Analysis of Linear Discrete Time Systems with Time Delay in State

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Wenguang Luo
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Delay ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

The controllability issues for linear discrete-time systems with delay in state are addressed. By introducing a new concept, the minimum controllability realization index (MinCRI), the characteristic of controllability is revealed. It is proved that the MinCRI of a system with state delay exists and is finite. Based on this result, a necessary and sufficient condition for the controllability of discrete-time linear systems with state delay is established.

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