scholarly journals Finite-Time Stability and Stabilization of Itô-Type Stochastic Singular Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhiguo Yan ◽  
Weihai Zhang
Keyword(s):  
Stochastic Stability ◽  
Finite Time ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Time Stability ◽  
Finite Time Stability ◽  
Stability And Stabilization ◽  
Stochastic Singular Systems

This paper is concerned with the finite-time stability and stabilization problems for linear Itô stochastic singular systems. The condition of existence and uniqueness of solution to such class of systems are first given. Then the concept of finite-time stochastic stability is introduced, and a sufficient condition under which an Itô stochastic singular system is finite-time stochastic stable is derived. Moreover, the finite-time stabilization is investigated, and a sufficient condition for the existence of state feedback controller is presented in terms of matrix inequalities. In the sequel, an algorithm is given for solving the matrix inequalities arising from finite-time stochastic stability (stabilization). Finally, two examples are employed to illustrate our results.

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.

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.

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.

scholarly journals Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Minsong Zhang
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Time Stability ◽  
Quadratic Systems ◽  
Finite Time Stability ◽  
Jump Time ◽  
Stability And Stabilization ◽  
Finite Time Stabilization

This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs) and linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methodology.

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