6533b85bfe1ef96bd12ba9d8
RESEARCH PRODUCT
Analysis of singular bilinear systems using Walsh functions
Frank L. LewisWieslaw MarszalekBasil G. Mertziossubject
Lyapunov functionRegular singular pointMathematical analysisGeneral EngineeringBilinear interpolationBilinear formsymbols.namesakeSingular solutionWalsh functionsymbolsApplied mathematicsLyapunov equationMathematicsSingular point of an algebraic varietydescription
The use of Walsh functions to analyse singular bilinear systems is investigated. It is shown that the nonlinear implicit differential system equation may be converted to a set of linear algebraic Lyapunov equations to be solved iteratively for the coefficients of the semistate x(t) in terms of the Walsh basis functions. Solution of the iterative algorithm is uniformly convergent to the exact solution of the algebraic generalised Lyapunov equation of the singular bilinear system. The present method is slightly more complicated than a similar one arising from the analysis of linear singular systems. In fact, it is a hybrid between the analyses of usual linear singular and bilinear regular systems.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1991-01-01 | IEE Proceedings D Control Theory and Applications |