On Zeros of Discrete-Time Models for Collocated Mass-Damper-Spring Systems

2004 ◽  
Vol 126 (1) ◽  
pp. 205-210 ◽  
Author(s):  
Mitsuaki Ishitobi ◽  
Shan Liang
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Sampling Period ◽  
Sufficient Condition ◽  
Time System ◽  
Time Model ◽  
Discrete Time Model ◽  
Mass Damper ◽  
Approximate Expressions ◽  
Continuous Time System

When a continuous-time system is discretized using the zero-order hold, there is no simple relation which shows how the zeros of the continuous-time system are transformed by sampling. In this paper, for a discrete-time model of a collocated mass-damper-spring system, the asymptotic behavior of the zeros is analyzed with respect to the sampling period and the linear approximate expressions are given. In addition, the linear approximate expressions lead to a sufficient condition for all the zeros of the discrete-time model to lie inside the unit circle for sufficiently small sampling periods. The sufficient condition is satisfied when a damping matrix is positive definite. Moreover, an example is shown to illustrate the validity of the linear approximations. Finally, a comment for a noncollocated system is presented.

scholarly journals Extreme stability and almost periodicity in continuous and discrete neuronal models with finite delays

2002 ◽  
Vol 44 (2) ◽  
pp. 261-282 ◽  
Author(s):  
S. Mohamad ◽  
K. Gopalsamy
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Model Neuron ◽  
Sufficient Conditions ◽  
External Stimulus ◽  
Input Stimulus ◽  
Time System ◽  
Time Model ◽  
Discrete Time Model ◽  
Continuous Time System

We consider the dynamical characteristics of a continuous-time isolated Hopfield-type neuron subjected to an almost periodic external stimulus. The model neuron is assumed to be dissipative having finite time delays in the process of encoding the external input stimulus and recalling the encoded pattern associated with the external stimulus. By using non-autonomous Halanay-type inequalities we obtain sufficient conditions for the hetero-associative stable encoding of temporally non-uniform stimuli. A brief study of a discrete-time model derived from the continuous-time system is given. It is shown that the discrete-time model preserves the stability conditions of the continuous-time system.

A Discrete-Time Model for Lotka-Volterra Equations With Preserved Stability of Equilibria

2013 ◽  
Author(s):  
Triet Nguyen-Van ◽  
Noriyuki Hori
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Equilibrium Points ◽  
Volterra Equations ◽  
Time System ◽  
Time Model ◽  
Discrete Time Model ◽  
Stability And Instability ◽  
Discrete Time Models ◽  
Continuous Time System

A Lotka-Volterra differential equation is discretized using a method proposed recently by the same authors for nonlinear autonomous systems and the stability of equilibrium points of the resulting discrete-time model is investigated. It is shown that when Jacobian matrix of the nonlinear equation is invertible, the equilibrium points of the model are identical to those of the original continuous-time system, and their asymptotic stability and instability are retained for any sampling period. While the method can be applied to any Lotka-Volterra types, simulation results are presented for a competitive-type example, where the continuous-time system and their discrete-time models obtained by the forward-difference, Mickens’, Kahan’s, and the proposed methods are compared. They illustrate that, in general, the proposed model performs better than other discrete-time models.

DISCRETE TIME REPRESENTATIONS OF COINTEGRATED CONTINUOUS TIME MODELS WITH MIXED SAMPLE DATA

2009 ◽  
Vol 25 (4) ◽  
pp. 1030-1049 ◽  
Author(s):  
Marcus J. Chambers
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Time System ◽  
Time Model ◽  
Stochastic Trends ◽  
Sample Data ◽  
Flow Variables ◽  
Mixed Stock ◽  
Gaussian Estimation ◽  
Continuous Time System

This paper derives an exact discrete time representation corresponding to a triangular cointegrated continuous time system with mixed stock and flow variables and observable stochastic trends. The discrete time model inherits the triangular structure of the underlying continuous time system and does not suffer from the apparent excess differencing that has been found in some related work. It can therefore serve as a basis for the study of the asymptotic sampling properties of estimators of the model's parameters. Some further analytical and computational results that enable Gaussian estimation to be implemented are also provided.

EXACT LINEARIZATION AND DISCRETIZATION OF NONLINEAR SYSTEMS SATISFYING A LAGRANGE PDE CONDITION

2011 ◽  
Vol 35 (2) ◽  
pp. 215-228 ◽  
Author(s):  
Takashi Sakamoto ◽  
Noriyuki Hori ◽  
Yoshimasa Ochi
Keyword(s):  
Differential Equation ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Condition ◽  
Exact Linearization ◽  
Time Model ◽  
Discrete Time Model ◽  
Exponential Transformation ◽  
Sampling Intervals ◽  
Associated Conditions

A sufficient condition for exact linearization of a nonlinear system via an exponential transformation is obtained as a Lagrange partial differential equation. When its solution can be found, the transformation is determined such that the nonlinear systemis exactly converted into a linear system with arbitrary dynamics. When the transformation is invertible, this technique can be applied to exact discretization. Several examples are given to demonstrate the linearization and discretization processes and associated conditions. Asimulation result is presented to show that, under proper conditions, the obtained discrete-time model gives values that are identical to the continuous-time original at discrete-time instants for any sampling intervals.

scholarly journals DISCRETE TIME REPRESENTATION OF CONTINUOUS TIME ARMA PROCESSES

2011 ◽  
Vol 28 (1) ◽  
pp. 219-238 ◽  
Author(s):  
Marcus J. Chambers ◽  
Michael A. Thornton
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Time System ◽  
Time Model ◽  
Time Representation ◽  
Sunspot Data ◽  
Mixed Stock ◽  
Continuous Time System

This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.

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.

Birth and death processes with random environments in continuous time

1981 ◽  
Vol 18 (01) ◽  
pp. 19-30 ◽  
Author(s):  
Robert Cogburn ◽  
William C. Torrez
Keyword(s):  
Discrete Time ◽  
Random Environment ◽  
Continuous Time ◽  
Death Process ◽  
Random Environments ◽  
Birth And Death Process ◽  
Time Model ◽  
Birth And Death Processes ◽  
Discrete Time Model ◽  
Extinction Probabilities

A generalization to continuous time is given for a discrete-time model of a birth and death process in a random environment. Some important properties of this process in the continuous-time setting are stated and proved including instability and extinction conditions, and when suitable absorbing barriers have been defined, methods are given for the calculation of extinction probabilities and the expected duration of the process.

QUEUE CONTROL UNDER TIME-VARIANT DELAYS: A DISCRETE TIME SYSTEM APPROACH

2002 ◽  
Vol 11 (02) ◽  
pp. 187-211
Author(s):  
PETER H. BAUER ◽  
MIHAIL L. SICHITIU ◽  
KAMAL PREMARATNE
Keyword(s):  
Control Systems ◽  
Communication Networks ◽  
Discrete Time ◽  
System Approach ◽  
Discrete Time System ◽  
System Delay ◽  
Time System ◽  
Time Model ◽  
Discrete Time Model ◽  
Stability Results

This paper introduces a discrete time model for time-variant delays and investigates the very nature of such delays. It is shown that a linear system-delay interface is a system theoretic necessity for the construction of composite linear systems with time-variant delays. Based on this analysis, two interfaces of particular importance are presented and used to obtain new, simple to check stability results for queue control systems. The relevance of the presented modeling and stability results on queue control systems to QoS control in modern communication networks is illustrated via several examples.

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