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.

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.

Finite-time guaranteed cost controller design for uncertain linear continuous-time singular systems

2019 ◽  
Vol 41 (12) ◽  
pp. 3507-3515 ◽  
Author(s):  
Bo Li ◽  
Songlin Wo ◽  
Junjie Zhao ◽  
Xuejing Ren
Keyword(s):  
Continuous Time ◽  
Finite Time ◽  
Closed Loop ◽  
Controller Design ◽  
Singular Systems ◽  
Singular System ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Guaranteed Cost ◽  
Bounded Uncertainties

This article concerns the finite-time robust guaranteed cost control problem for a class of linear continuous-time singular systems with norm-bounded uncertainties. In this study, the problem is to design a state feedback controller such that the closed-loop system is finite-time stable, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. By constructing an appropriate Lyapunov function, a sufficient condition for the finite-time robust stability of the system based on linear matrix inequality (LMI) is established. Furthermore, the sufficient condition for the existence of the guaranteed cost controller is formulated in terms of LMIs, which can make the closed-loop uncertain singular system finite-time robust stable. Finally, two numerical examples are given for illustration of the proposed theoretical results.

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 for a Class of Underactuated Systems Subject to Time-Varying Disturbance

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Jie Wu ◽  
Dan Yang ◽  
Xinyi He ◽  
Xiaodi Li
Keyword(s):  
Finite Time ◽  
Design Methodology ◽  
Controller Design ◽  
Underactuated Systems ◽  
Local Form ◽  
Sufficient Condition ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Convergence Performance

Based on the classical finite-time stability theory, the problem of finite-time stability (FTS) for time-varying nonlinear systems is investigated in this paper. Several FTS theorems involving global form and local form are presented, and an estimate of the settling-time of such systems is obtained. As an application, we consider the problem of asymptotic stabilization of the Brockett integrator subject to time-varying disturbance. By the switched finite-time controller design methodology, we establish a sufficient condition to guarantee the relative asymptotic stability. For Brockett-like integrator subject to time-varying disturbance, we achieve better convergence performance. Examples and their simulations are given to demonstrate the applicability of the proposed results.

L2 norm-based finite-time stability and boundedness of singular distributed parameter systems with parabolic type

2020 ◽  
pp. 095965182096689
Author(s):  
Xingyu Zhou ◽  
Haoping Wang ◽  
Yang Tian
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Parabolic Type ◽  
Distributed Parameter Systems ◽  
Temperature Control System ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Time Stability ◽  
Finite Time Stability ◽  
L2 Norm

In this study, the problem of finite-time stability and boundedness for parabolic singular distributed parameter systems in the sense of [Formula: see text] norm is investigated. First, two new results on [Formula: see text] norm-based finite-time stability and finite-time boundedness for above-mentioned systems, inspired by the light of partial differential equations theory and Lyapunov functional method, are presented. Then, some sufficient conditions of [Formula: see text] norm-based finite-time stability and boundedness are established by virtue of differential inequalities and linear matrix inequalities. Furthermore, the distributed state feedback controllers are constructed to guarantee the [Formula: see text] norm-based finite-time stable and bounded of the closed-loop singular distributed parameter systems. Finally, numerical simulations on a specific numerical example and the building temperature control system equipped with air conditioning are given to demonstrate the validity of the proposed methods.

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