The discrete-time strictly bounded-real lemma and the computation of positive definite solutions to the 2-D Lyapunov equation

1989 ◽  
Vol 36 (6) ◽  
pp. 830-837 ◽  
Author(s):  
P. Agathoklis ◽  
E.I. Jury ◽  
M. Mansour
Keyword(s):  
Discrete Time ◽  
Lyapunov Equation ◽  
Positive Definite ◽  
Bounded Real Lemma

scholarly journals Noise-Resistant Discrete-Time Neural Dynamics for Computing Time-Dependent Lyapunov Equation

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 45359-45371 ◽  
Author(s):  
Qiuhong Xiang ◽  
Weibing Li ◽  
Bolin Liao ◽  
Zhiguan Huang
Keyword(s):  
Discrete Time ◽  
Computing Time ◽  
Lyapunov Equation ◽  
Time Dependent ◽  
Neural Dynamics

scholarly journals H2/H∞ Control for MJLS with Infinite Markov Chain

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Ting Hou ◽  
Jie Wang ◽  
Yueying Liu ◽  
Xiao Shen
Keyword(s):  
Markov Chain ◽  
Control Problem ◽  
Discrete Time ◽  
Control Design ◽  
Finite Horizon ◽  
Bounded Real Lemma ◽  
Infinite Set

With the help of a stochastic bounded real lemma, we deal with finite horizon H2/H∞ control problem for discrete-time MJLS, whose Markov chain takes values in an infinite set. Besides, a unified control design for H2, H∞, and H2/H∞ is given.

SOLVING DISCRETE-TIME LYAPUNOV EQUATIONS FOR THE CHOLESKY FACTOR ON A SHARED MEMORY MULTIPROCESSOR

1996 ◽  
Vol 06 (03) ◽  
pp. 365-376 ◽  
Author(s):  
JOSE M. CLAVER ◽  
VICENTE HERNANDEZ ◽  
ENRIQUE S. QUINTANA
Keyword(s):  
Parallel Algorithms ◽  
Shared Memory ◽  
Discrete Time ◽  
Lyapunov Equation ◽  
Lyapunov Equations ◽  
Parallel Solution ◽  
Cholesky Factor ◽  
Large Order ◽  
Shared Memory Multiprocessor

In this paper we study the parallel solution of the discrete-time Lyapunov equation. Two parallel fine and medium grain algorithms for solving dense and large order equations [Formula: see text] on a shared memory multiprocessor are presented. They are based on Hammarling’s method and directly obtain the Cholesky factor of the solution. The parallel algorithms work following an antidiagonal wavefront. In order to improve the performance, column-block-oriented and wrap-around algorithms are used. Finally, combined fine and medium grain parallel algorithms are presented.

On the sensitivity of the coupled discrete-time Lyapunov equation

2001 ◽  
Vol 46 (4) ◽  
pp. 659-664 ◽  
Author(s):  
A. Czornik ◽  
A. Swierniak
Keyword(s):  
Discrete Time ◽  
Lyapunov Equation

scholarly journals Evolutionary dynamics in discrete time for the perturbed positive definite replicator equation

2021 ◽  
Vol 62 ◽  
pp. 148-184
Author(s):  
Amie Albrecht ◽  
Konstantin Avrachenkov ◽  
Phil Howlett ◽  
Geetika Verma
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Evolutionary Dynamics ◽  
Positive Definite ◽  
Genotype Distribution ◽  
Replicator Equation ◽  
System Matrix ◽  
Discrete Time System ◽  
Time System ◽  
Time Dynamics

The population dynamics for the replicator equation has been well studied in continuous time, but there is less work that explicitly considers the evolution in discrete time. The discrete-time dynamics can often be justified indirectly by establishing the relevant evolutionary dynamics for the corresponding continuous-time system, and then appealing to an appropriate approximation property. In this paper we study the discrete-time system directly, and establish basic stability results for the evolution of a population defined by a positive definite system matrix, where the population is disrupted by random perturbations to the genotype distribution either through migration or mutation, in each successive generation. doi: 10.1017/S1446181120000140

scholarly journals Interval criterion for stability analysis of discrete-time nonlinear systems with partial state saturation nonlinearities

2006 ◽  
Vol 19 (2) ◽  
pp. 271-286
Author(s):  
Lubomir Kolev ◽  
Simona Filipova-Petrakieva ◽  
Valeri Mladenov
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Interval Uncertainties ◽  
Partial State ◽  
Definite Interval ◽  
Outer Bounds ◽  
State Saturation

A generalization of sufficient conditions for global asymptotic stability of the equilibrium of discrete-time nonlinear systems with saturation non linearity's on part of the states in the case of interval uncertainties is considered. When using quadratic form Lyapunov functions, sufficient conditions based on the positive definite interval matrices are presented. In order to check this, a recently proposed method for determining the outer bounds of eigenvalues ranges is used. A numerical example illustrating the applicability of the method suggested is solved in the end of the paper.

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