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.

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.

scholarly journals Absolute stability of a class of fractional positive nonlinear systems

2019 ◽  
Vol 29 (1) ◽  
pp. 93-98 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Discrete Time Systems ◽  
The Absolute ◽  
Necessary And Sufficient ◽  
Time Systems

Abstract The positivity and absolute stability of a class of fractional nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of fractional positive nonlinear systems are also given.

scholarly journals Fractional descriptor standard and positive discrete-time nonlinear systems

2015 ◽  
Vol 63 (3) ◽  
pp. 651-655
Author(s):  
T. Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Linear Part ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Example ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

AbstractA method of analysis of the fractional descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on a numerical example.

scholarly journals An approach to the analysis of observability and controllability in nonlinear systems via linear methods

2012 ◽  
Vol 22 (3) ◽  
pp. 507-522 ◽  
Author(s):  
Alexey Zhirabok ◽  
Alexey Shumsky
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Dynamic Systems ◽  
Linear Part ◽  
Sufficient Conditions ◽  
Nonlinear Dynamic Systems ◽  
New Approach ◽  
Discrete Time Systems ◽  
Programming Systems ◽  
Time Systems

Abstract The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g.,Matlab. Sufficient conditions are given for nonlinear unobservability/uncontrollability analysis. To apply these conditions, one isolates the linear part of the system which is checked to be unobservable/uncontrollable and, if the answer is positive, it is examined whether or not existing nonlinear terms violate the unobservability/uncontrollability property.

scholarly journals On two theorems regarding exponential stability

2011 ◽  
Vol 5 (2) ◽  
pp. 240-258 ◽  
Author(s):  
Viet Hai
Keyword(s):  
Dynamical Systems ◽  
Exponential Stability ◽  
Discrete Time ◽  
Discrete Time Systems ◽  
Stability Of Dynamical Systems ◽  
Time Systems

There are two remarkable results in the theory of stability of dynamical systems which were obtained by R. Datko in 1970 and E.A. Barbashin in 1967. After the seminal researches of Datko and Barbashin, there have been a great number of works devoted to this results. For the case of discrete-time systems analogous results have been obtained. This paper will give the new versions which unify the discrete-time versions of Barbashin's theorem and Datko's theorem.

scholarly journals Robust Stability Analysis for Uncertain Switched Discrete-Time Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Yali Dong
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
State Parameter ◽  
Matrix Inequality ◽  
Lyapunov Stability Theorem ◽  
Switching Law ◽  
Discrete Time Systems ◽  
Robust Stability Analysis ◽  
Time Systems

This paper is concerned with the robust stability for a class of switched discrete-time systems with state parameter uncertainty. Firstly, a new matrix inequality considering uncertainties is introduced and proved. By means of it, a novel sufficient condition for robust stability of a class of uncertain switched discrete-time systems is presented. Furthermore, based on the result obtained, the switching law is designed and has been performed well, and some sufficient conditions of robust stability have been derived for the uncertain switched discrete-time systems using the Lyapunov stability theorem, block matrix method and inequality technology. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

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