scholarly journals Input–output admissibility and exponential trichotomy of difference equations

2011 ◽  
Vol 380 (1) ◽  
pp. 17-32 ◽  
Author(s):  
Adina Luminiţa Sasu ◽  
Bogdan Sasu
Keyword(s):  
Difference Equations ◽  
Input Output ◽  
Exponential Trichotomy

TRANSFER EQUIVALENCE AND REALIZATION OF NONLINEAR HIGHER ORDER INPUT/OUTPUT DIFFERENCE EQUATIONS USING MATHEMATICA

1999 ◽  
Vol 09 (01n02) ◽  
pp. 23-35 ◽  
Author(s):  
ÜLLE KOTTA ◽  
MARIS TÕNSO
Keyword(s):  
Control Systems ◽  
Difference Equations ◽  
Space Form ◽  
Higher Order ◽  
Nonlinear Control Systems ◽  
Input Output ◽  
Nonlinear Case ◽  
State Equations ◽  
Order Difference ◽  
Classical State

This paper presents a contribution to the development of symbolic computation tools for discrete-time nonlinear control systems. A set of functions is developed in Mathematica 3.0 that test if the higher order input/output difference equation is realizable in the classical state-space form, and for simple examples, also find such state equations. The approach relies on a new notion of equivalence of higher order difference equations which yields a minimal (i.e. accessible and observable) realization and generalizes the notion of transfer equivalence to the nonlinear case. The application of the developed functions is demonstrated on three examples obtained via identification.

scholarly journals Nonuniform Exponential Trichotomy for Linear Discrete-Time Systems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-qiu Song ◽  
Tian Yue ◽  
Dong-qing Li
Keyword(s):  
Exponential Stability ◽  
Banach Spaces ◽  
Discrete Time ◽  
Difference Equations ◽  
Exponential Dichotomy ◽  
Linear Difference Equations ◽  
Discrete Time Systems ◽  
Exponential Trichotomy ◽  
Time Systems

The aim of this paper is to give several characterizations for nonuniform exponential trichotomy properties of linear difference equations in Banach spaces. Well-known results for exponential stability and exponential dichotomy are extended to the case of nonuniform exponential trichotomy.

Transfer equivalence and realization of nonlinear higher order input–output difference equations

Automatica ◽  
2001 ◽  
Vol 37 (11) ◽  
pp. 1771-1778 ◽  
Author(s):  
Ü. Kotta ◽  
A.S.I. Zinober ◽  
P. Liu
Keyword(s):  
Difference Equations ◽  
Higher Order ◽  
Input Output

STABILITY RADII FOR IMPLICIT DIFFERENCE EQUATIONS

2009 ◽  
Vol 02 (01) ◽  
pp. 95-115 ◽  
Author(s):  
Benjawan Rodjanadid ◽  
Van Sanh Nguyen ◽  
Thu Ha Nguyen ◽  
Huu Du Nguyen
Keyword(s):  
Difference Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Difference Equations ◽  
Time Varying ◽  
Complex Stability ◽  
Input Output ◽  
Parameter Perturbations ◽  
Stability Radii

This paper is concerned with a formula of stability radii for a linear implicit difference equation (LIDEs for short) varying in time with index-1 under structured parameter perturbations. It is shown that the lp-real and complex stability radii of these systems coincide and they are given by a formula of input-output operators. The result is an extension of a previous result for time-varying ordinary differential equations [7].

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