Stability of delayed inertial neural networks on time scales: A unified matrix-measure approach
Qiang Xiao, Tingwen Huang
Abstract
This note introduces a unified matrix-measure concept to study the stability of a class of inertial neural networks with bounded time delays on time scales. The novel matrix-measure concept unifies the classic matrix-measure and the generalized matrix-measure concept. One sufficient global exponential stability criterion is obtained based on this key matrix-measure and no Lyapunov function is required. To make the stability performance better, another stability criterion in which more detailed information is involved has been acquired. The theoretical results in this note contain and extend some existing continuous-time and discrete-time works. A numerical example is given to show the validity of the results.
Topics & Concepts
Measure (data warehouse)Matrix (chemical analysis)Stability (learning theory)Inertial frame of referenceMathematicsExponential stabilityDiscrete time and continuous timeBounded functionArtificial neural networkComputer scienceLyapunov functionApplied mathematicsMathematical optimizationControl theory (sociology)Artificial intelligenceMathematical analysisData miningMachine learningNonlinear systemStatisticsComposite materialControl (management)Quantum mechanicsMaterials sciencePhysicsNeural Networks Stability and SynchronizationNeural Networks and ApplicationsNonlinear Dynamics and Pattern Formation