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Controllability and observability gramians parallel computation using GPU

Raczyński D, Stanisławski W.

Journal of Theoretical and Applied Computer Science

2012

Vol. 6, nr 1

47-66

Algorithms and parallel programs for the controllability and observability gramians computation of the Linear Time Invariant (LTI) systems using Lyapunov equation with an application of the NVIDIA general purpose Graphics Processing Unit (GPU), are presented in the paper. Parallel computing of the gramians on the basis of Lyapunov equation is justified for the large scale systems (n>104) due to the computational cost O(n3). The parallel performance of controllability gramians computation using NVIDIA graphics hardware GTX-465 have been compared with the performance obtained for MATLAB environment employing analogous algorithms. They have also been compared with the performance obtained for lyap function provided by MATLAB environment. The values of maximum computing acceleration were up to 20. The computations have been made on the basis of linearized models of the one-phase zone of a once-through boiler obtained with the finite elements method. The orders of the models were being adapted within the range between 30 and 4200.

Application of Lyapunov equation to analysis of random vibration of structure with tuned mass dampers

Lewandowski R., Grzymisławska J.

Vibrations in Physical Systems

2008

Vol. 23

229--234

In this paper the Lyapunov equation is used to analyse random vibration of building structure. The structures with mass dampers are considered. The excitation forces which are functions of fluctuations of wind velocity are treated as random forces. Lyapunov equation is used to determine root mean square of displacements. Results of example calculation are presented and briefly discussed.

The alpha-scalar Diagonal Stability of Some Classes of Matrices

Wanat M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2003

Vol. 51, nr 1

105-112

In the paper we formulate the sufficient condition which must satisfy an irreducible acyclic matrix A to be alpha-scalar diagonally stable. Moreover we consider the existence of positive definite diagonal matrix C and positive definite alpha-scalar matrix D such that DA+ATD=C. These conditions are the generalizations of several theorems which are the necessary and sufficient condition which must satisfy square matrix A to exist positive diagonal matrices C and D such that DA+ATD=C.