Title :
On the "SIR"s ("Signal"-to-"Interference"-Ratio) in Discrete-Time Autonomous Linear Networks
Author_Institution :
Control Eng. Lab., Helsinki Univ. of Technol., Espoo, Finland
Abstract :
A Hopfield-like neural network, called SALU-SIR,whose system weight matrix is symmetric is presented with its mathematical analysis in. However, what happens if the system matrix is unsymmetric? Is the system still stable in the unsymmetric case? In this paper, we address these important questions, whose answer is paramount especially when the system is to be implemented in practice.The underlying linear system of the proposed network is x(k+1) = Ax(k)+b where A is any real square unsymmetric matrix with linearly independent eigenvectors whose largest eigenvalue is real and its norm is larger than 1, and vector b is constant. Our investigations in this paper show that (i) the unsymmetric case is also stable; (ii) the unsymmetric case yields state-specific ultimate SIRs as compared to the system-specific ultimate SIR in the symmetric case, which allows us to design more complex systems. (iii) the ultimate ¿SIR¿s in the investigated unsymmetric matrix A case are equal to aii¿max-aii , i = 1, 2, . . . , N, where Nis the number of states, aii is the diagonal elements of matrix A, and ¿max is the (single or multiple) eigenvalue with maximum norm.Possible applications include binary associative memory systems, image restoration, etc in the area of artificial intelligence and cognition.
Keywords :
Hopfield neural nets; discrete time systems; neurocontrollers; nonlinear control systems; Hopfield neural network; SALU-SIR system; discrete-time autonomous linear networks; real square unsymmetric matrix; signal-to-interference ratio; system weight matrix; Associative memory; Eigenvalues and eigenfunctions; Hopfield neural networks; Image restoration; Interference; Linear systems; Mathematical analysis; Neural networks; Symmetric matrices; Vectors; Autonomous Discrete-Time Linear Systems; Hopfield-like Neural network.; Signal to Interference Ratio (SIR);
Conference_Titel :
Future Computing, Service Computation, Cognitive, Adaptive, Content, Patterns, 2009. COMPUTATIONWORLD '09. Computation World:
Conference_Location :
Athens
Print_ISBN :
978-1-4244-5166-1
Electronic_ISBN :
978-0-7695-3862-4
DOI :
10.1109/ComputationWorld.2009.115