** Viðburði frestað ** Málstofa verkfræðistofnunar - Anna Soffía Hauksdóttir

Anna Soffía Hauksdóttir, prófessor við Rafmagns- og tölvuverkfræðideild HÍ, heldur fyrirlesturinn  Closed Form Expressions of Linear System Responses - Continuous time differential equations and discrete time difference equations (Lausnir línulegra diffurjafna og mismunajafna á lokuðu formi).

Fyrirlesturinn fer fram á ensku.

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Ágrip:

The main motivation is to develop closed form expressions of linear time invariant (LTI) system responses - continuous time as well as discrete time and to highlight the close relationship between the two. The closed forms result in efficient computation of the responses of moderate sized systems, directly at any time without timestepping in the case of polynomial or harmonic input. We relate these responses to basic responses and subsequently to the fundamental solutions of the underlying equations, i.e., continuous time differential equations and discrete time difference equations.

The closed forms form the basis of deriving directly, e.g., PID-type controllers for linear systems by optimization, closed form Gramians, the matrix exponent $e^{At}$, etc. In addition, these results have applications in all areas where LTI differential equations and discrete time difference equations pop up. Further, they may have applications in hybrid systems as well, i.e., in applications having irregular data sampling.