scholarly journals Stabilization Analysis for the Switched Large-Scale Discrete-Time Systems via the State-Driven Switching

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Chi-Jo Wang ◽  
Juing-Shian Chiou
Keyword(s):  
Lyapunov Stability ◽  
Discrete Time ◽  
Large Scale ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Time Systems ◽  
Switching Method ◽  
Time Systems

A criterion of stabilization for the switched large-scale discrete-time system is deduced by employing state-driven switching method and the Lyapunov stability theorem. This particular method especially can be applied to cases when all individual subsystems are unstable.

CHAOTIFICATION OF DISCRETE-TIME SYSTEMS USING NEURONS

2004 ◽  
Vol 14 (04) ◽  
pp. 1405-1411 ◽  
Author(s):  
H. S. KWOK ◽  
WALLACE K. S. TANG
Keyword(s):  
Computer Simulations ◽  
Discrete Time ◽  
Activation Function ◽  
Feedback Signal ◽  
Discrete Time System ◽  
Hyperbolic Tangent ◽  
Time System ◽  
Discrete Time Systems ◽  
Arbitrary Dimensions ◽  
Time Systems

In this paper, a neuron is introduced for chaotifying nonchaotic discrete-time systems with arbitrary dimensions. By modeling the neuron with a hyperbolic tangent activation function, a scalar feedback signal expressed in a linear combination of the neuron outputs is used. Chaos can then be generated from the controlled discrete-time system. The existence of chaos is verified by both theoretical proof and computer simulations.

The MMVC for the Nth Order Linear Discrete-Time Systems under Prospective Strong Intervention

2014 ◽  
Vol 496-500 ◽  
pp. 1630-1633
Author(s):  
Qiu Ju Wang ◽  
Ru Dong Gai
Keyword(s):  
Discrete Time ◽  
System Model ◽  
Discrete Time System ◽  
Time System ◽  
Order Linear ◽  
First Order ◽  
Discrete Time Systems ◽  
Minimal Variance ◽  
Two Parameters ◽  
Time Systems

This paper is devoted to the issue of the modified minimal variance control (MMVC)for the nth linear discrete-time systems under prospective strong intervention (PSI). At fist, establish the Nth order linear discrete time system model. Based on the research of the first-order linear discrete time systems under PSI with the constraint of minimal variance control, the algorithm is extended to the nth order linear discrete time systems, so one can get MMVC of the nth order linear discrete-time systems with constraint under PSI and by introducing two parameters to proof.

scholarly journals HYPERCHAOTIC DYNAMICS OF A NEW FRACTIONAL DISCRETE-TIME SYSTEM

Fractals ◽  
2021 ◽  
pp. 2140034
Author(s):  
AMINA-AICHA KHENNAOUI ◽  
ADEL OUANNAS ◽  
SHAHER MOMANI ◽  
ZOHIR DIBI ◽  
GIUSEPPE GRASSI ◽  
...  
Keyword(s):  
Discrete Time ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Time Systems ◽  
Simulation Results ◽  
Time Systems ◽  
First Time

In recent years, some efforts have been devoted to nonlinear dynamics of fractional discrete-time systems. A number of papers have so far discussed results related to the presence of chaos in fractional maps. However, less results have been published to date regarding the presence of hyperchaos in fractional discrete-time systems. This paper aims to bridge the gap by introducing a new three-dimensional fractional map that shows, for the first time, complex hyperchaotic behaviors. A detailed analysis of the map dynamics is conducted via computation of Lyapunov exponents, bifurcation diagrams, phase portraits, approximated entropy and [Formula: see text] complexity. Simulation results confirm the effectiveness of the approach illustrated herein.

Exponential Stability Analysis of Fixed Point Interfered Nonlinear Digital Systems in the Presence of Quantization and Overflow Constraints

2020 ◽  
Vol 19 (04) ◽  
pp. 2050040
Author(s):  
Saddam Hussain Malik ◽  
Muhammad Tufail ◽  
Muhammad Rehan ◽  
Shakeel Ahmed
Keyword(s):  
Fixed Point ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Discrete Time ◽  
Digital Systems ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Time Systems ◽  
Digital Hardware ◽  
Time Systems

Finite word length is a practical limitation when discrete-time systems are implemented by using digital hardware. This restriction degrades the performance of a discrete-time system and may even lead it toward instability. This paper, addresses the stability and disturbance attenuation performance analysis of nonlinear discrete-time systems under the influence of energy-bounded external interferences when such systems are subjected to quantization and overflow effects of fixed point hardware. The proposed methodology, in comparison with previous paper, describes exponential stability for the nonlinear discrete-time systems by considering composite nonlinearities of digital hardware. The proposed criteria that ensure exponential stability and [Formula: see text] performance index for the digital systems under consideration are presented in the form of a set of linear matrix inequalities (LMIs) by exploiting Lyapunov stability theory, Lipschitz condition and sector conditions for different types of commonly used quantization and overflow arithmetic properties, and the results are validated for recurrent neural networks. Furthermore, novel stability analysis results for a nonlinear discrete-time system under hardware constraints can also be observed as a special case of the proposed criteria.

scholarly journals Controlling the Stochastic Sensitivity in Nonlinear Discrete-Time Systems with Incomplete Information

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Lev Ryashko ◽  
Irina Bashkirtseva
Keyword(s):  
Incomplete Information ◽  
Discrete Time ◽  
Large Amplitude ◽  
Matrix Equations ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Time Systems ◽  
Stochastic Sensitivity ◽  
Quadratic Matrix ◽  
Time Systems

For stochastic nonlinear discrete-time system with incomplete information, a problem of the stabilization of equilibrium is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations.

scholarly journals Losslessness of Nonlinear Stochastic Discrete-Time Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Xikui Liu ◽  
Yan Li ◽  
Ning Gao
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Zero Dynamics ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

This paper will study stochastic losslessness theory for nonlinear stochastic discrete-time systems, which are expressed by the Itô-type difference equations. A necessary and sufficient condition is developed for a nonlinear stochastic discrete-time system to be lossless. By the stochastic lossless theory, we show that a nonlinear stochastic discrete-time system can be lossless via state feedback if and only if it has relative degree0,…,0and lossless zero dynamics. The effectiveness of the proposed results is illustrated by a numerical example.

scholarly journals W-Stability of Multistable Nonlinear Discrete-Time Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Zhishuai Ding ◽  
Guifang Cheng ◽  
Xiaowu Mu
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
Discrete Dynamical Systems ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Converse Theorem ◽  
Discrete Time Systems ◽  
New Type ◽  
Time Systems

Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion ofW-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.

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