The optimal projection equations for finite-dimensional fixed-order ℋ2-optimal control of infinite-dimensional discrete-time systems

1995 ◽  
Vol 61 (3) ◽  
pp. 641-655
Author(s):  
FLORIN DAN BARB ◽  
WILLEM L. DE KONING
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Discrete Time Systems ◽  
Optimal Projection ◽  
Fixed Order ◽  
Projection Equations ◽  
Time Systems

scholarly journals Stability criteria for positive linear discrete-time systems

Positivity ◽  
2021 ◽  
Author(s):  
Jochen Glück ◽  
Andrii Mironchenko
Keyword(s):  
Banach Spaces ◽  
Discrete Time ◽  
Positive Cone ◽  
Stability Criteria ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Discrete Time Systems ◽  
Small Gain ◽  
Time Systems ◽  
Ordered Banach Spaces

AbstractWe prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have played an important role in the finite-dimensional systems theory, but are relatively unexplored in the infinite-dimensional setting, yet. Our results are applicable to discrete-time systems in ordered Banach spaces that have a normal and generating positive cone. Moreover, we show that our stability criteria can be considerably simplified if the cone has non-empty interior or if the operator under consideration is quasi-compact. To place our results into context we include an overview of known stability criteria for linear (and not necessarily positive) operators and provide full proofs for several folklore characterizations from this domain.

scholarly journals Stabilization of strictly dissipative discrete time systems with discounted optimal control

Automatica ◽  
2018 ◽  
Vol 93 ◽  
pp. 311-320 ◽  
Author(s):  
Vladimir Gaitsgory ◽  
Lars Grüne ◽  
Matthias Höger ◽  
Christopher M. Kellett ◽  
Steven R. Weller
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Discrete Time Systems ◽  
Time Systems
Sign in / Sign up

Export Citation Format

Share Document