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.

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 Stability of Stochastic Discrete-Time Neural Networks with Discrete Delays and the Leakage Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Liyuan Hou ◽  
Hong Zhu
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Delays ◽  
The Stability

This paper investigates the stability of stochastic discrete-time neural networks (NNs) with discrete time-varying delays and leakage delay. As the partition of time-varying and leakage delay is brought in the discrete-time system, we construct a novel Lyapunov-Krasovskii function based on stability theory. Furthermore sufficient conditions are derived to guarantee the global asymptotic stability of the equilibrium point. Numerical example is given to demonstrate the effectiveness of the proposed method and the applicability of the proposed method.

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.

A Generalization of Poincaré’s Theorem to Periodic Hybrid and Impulsive Dynamical Systems

2001 ◽  
Author(s):  
V. Chellaboina ◽  
S. G. Nersesov ◽  
W. M. Haddad
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Discrete Time ◽  
Discrete Time System ◽  
Time System ◽  
Stability Of Periodic Orbits ◽  
Poincaré Return Map ◽  
The Stability ◽  
Time Periodic ◽  
Special Case

Abstract Poincaré’s method is well known for analyzing the stability of continuous-time periodic dynamical systems by studying the stability properties of a fixed point as an equilibrium point of a discrete-time system. In this paper we generalize Poincaré’s method to dynamical systems possessing left-continuous flows to address the stability of limit cycles and periodic orbits of left-continuous, hybrid, and impulsive dynamical systems. It is shown that resetting manifold (which gives rise to the state discontinuities) provides a natural hyperplane for defining a Poincaré return map. In the special case of impulsive dynamical systems, we show the Poincaré map replaces an nth-order impulsive dynamical system by an (n − 1)th-order discrete-time system for analyzing the stability of periodic orbits.

scholarly journals Robust stability of discrete-time systems of difference equations (Removed from Archives)

2007 ◽  
Vol 38 (3) ◽  
pp. 205-208 ◽  
Author(s):  
Ziad Zahreddine
Keyword(s):  
Characteristic Polynomial ◽  
Robust Stability ◽  
Discrete Time ◽  
Difference Equations ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Schur Stability

This paper deals with the robust stability of discrete-time systems of difference equations. Given the nominal characteristic polynomial of a certain discrete-time system, we determine the maximum allowable perturbation that such a polynomial can undergo while preserving the Schur stability of the corresponding system.

scholarly journals MOBIUS AND DELTA TRANSFORMS IN THE UNIFICATION OF CONTINUOUS-DISCRETE SPACES

2013 ◽  
Vol 12 (2) ◽  
pp. 15
Author(s):  
T. BAKHTIAR ◽  
S. SAMSURIZAL ◽  
N. ALIATININGTYAS
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Complex Space ◽  
Discrete Time System ◽  
Time System ◽  
The Laplace Transform ◽  
The Stability ◽  
Discrete Spaces ◽  
Bode Integral ◽  
Continuous Time System

It is well-known that in control theory the stability region of continuous- time system is laid in the left half plane of complex space, while that of discrete-time system is dwelled inside a unit circle. The former fact might be shown by exploiting the Laplace transform and the later by utilizing the corresponding zeta transform. In this paper we revealed the connectivity of both regions by employing M¨obius transform. We also used the same transform to derive continuous/discrete-time counterpart of several existing results, including Bode integral and Poisson-Jensen formula. We then demonstrated their unification property by using delta transform. Some numerical examples were provided to verify our results.

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