scholarly journals Stability Analysis of Linear Systems under Time-Varying Samplings by a Non-Standard Discretization Method

Electronics ◽  
2018 ◽  
Vol 7 (11) ◽  
pp. 278 ◽  
Author(s):  
Xiefu Jiang ◽  
Zongming Yin ◽  
Jinjing Wu
Keyword(s):  
Linear Systems ◽  
Stability Criterion ◽  
Uncertain Systems ◽  
Closed Loop ◽  
Time Varying ◽  
Discretization Method ◽  
Sampled Data ◽  
Discrete Time System ◽  
Parameter Uncertainties ◽  
The Stability

This paper is concerned with the stability of linear systems under time-varying sampling. First, the closed-loop sampled-data system under study is represented by a discrete-time system using a non-standard discretization method. Second, by introducing a new sampled-date-based integral inequality, the sufficient condition on stability is formulated by using a simple Lyapunov function. The stability criterion has lower computational complexity, while having less conservatism compared with those obtained by a classical input delay approach. Third, when the system is subject to parameter uncertainties, a robust stability criterion is derived for uncertain systems under time-varying sampling. Finally, three examples are given to show the effectiveness of the proposed method.

scholarly journals Robust Stability of Uncertain Systems over Network with Bounded Packet Loss

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yafeng Guo ◽  
Tianhong Pan
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Stability Criterion ◽  
Packet Loss ◽  
Lyapunov Functional ◽  
Uncertain Systems ◽  
Discrete Time System ◽  
Time System ◽  
Numerical Examples ◽  
The Stability

This paper investigates the problem of robust stability of uncertain linear discrete-time system over network with bounded packet loss. A new Lyapunov functional is constructed. It can more fully utilize the characteristics of the packet loss; hence the established stability criterion is more effective to deal with the effect of packet loss on the stability. Numerical examples are given to illustrate the effectiveness and advantage of the proposed methods.

scholarly journals Advanced controller design for uncertain linear systems with time-varying delays via augmented zero equality approach

2021 ◽  
Author(s):  
YongGwon Lee ◽  
Youngjae Kim ◽  
Seungho Kim ◽  
Seunghoon Lee ◽  
Myeongjin Park ◽  
...  
Keyword(s):  
Linear Systems ◽  
Controller Design ◽  
Time Derivative ◽  
Linear Matrix ◽  
Feasible Region ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Controller Gain ◽  
The Stability ◽  
Uncertain Linear Systems

This paper deals with the stability analysis and controller design for linear systems with time-varying delays and parameter uncertainties. By choosing appropriate augmented Lyapunov-Krasovskii functionals, a set of Linear Matrix inequalities is derived to get advanced feasible region of stability, and controller gain matrices which guarantee the asymptotic stability of the concerned systems within maximum bound of time-delays and its time-derivative. To further reduce the conservatism of stabilization criterion a recently developed mathematical technique which constructed a new augmented zero equality is applied. Finally, two numerical examples are utilized to show the validity and superiority of the proposed methods.

Stability of real-time hybrid simulation involving time-varying delay and direct integration algorithms

2021 ◽  
pp. 107754632110016
Author(s):  
Liang Huang ◽  
Cheng Chen ◽  
Shenjiang Huang ◽  
Jingfeng Wang
Keyword(s):  
Real Time ◽  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Simulation ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Integration Algorithms ◽  
The Stability ◽  
Continuous Time System

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.

scholarly journals ℋ∞Performance and Stability Analysis of Linear Systems with Interval Time-Varying Delays and Stochastic Parameter Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Stability Analysis ◽  
Linear Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Interval Time ◽  
Stochastic Parameter ◽  
Stochastic Properties ◽  
Random Change

This paper deals with the problems ofℋ∞performance and stability analysis for linear systems with interval time-varying delays. It is assumed that the parameter uncertainties are of stochastic properties to represent random change of various environments. By constructing a newly augmented Lyapunov-Krasovskii functional, less conservative criteria of the concerned systems are introduced with the framework of linear matrix inequalities (LMIs). Four numerical examples are given to show the improvements over the existing ones and the effectiveness of the proposed methods.

Stability of Discrete-Time Switched Linear Systems with Saturation Arithmetic

2013 ◽  
Vol 427-429 ◽  
pp. 1319-1323
Author(s):  
Meng Hua Zhang ◽  
Xin Gong Cheng ◽  
Xi Ju Zong
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Stability Condition ◽  
Closed Loop ◽  
Switched Linear Systems ◽  
The Stability ◽  
Saturation Arithmetic ◽  
Theoretical Results

This paper addresses a strategy for the stability of discrete-time switched linear systems with saturation arithmetic. It is of closed-loop nature and is designed from the solution of what we called Lyapunov-Metzler inequalities from which the stability condition is expressed. The theoretical results are illustrated by means of examples.

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