Alkalmazott Analízis Szeminárium

A BME Matematika Intézet Analízis és Differenciálegyenletek Tanszékének közös Alkalmazott Analízis Szemináriuma 2016. őszén indult Faragó István (Differenciálegyenletek Tanszék) kezdeményezésére az MTA-ELTE Numerikus Analízis és Nagy Hálózatok Kutatócsoporttal együttműködésben. A szeminárium célja, hogy elősegítse egy alkalmazott analízissel (funkcionálanalízis, differenciálegyenletek, numerikus módszerek) foglalkozó kutatói kör kialakítását az intézeten belül. A szemináriummal fórumot szeretnénk biztosítani az alkalmazott analízissel foglalkozó matematikusok és az analízist alkalmazó kutatók számára az együtt gondolkodásra. További cél az érdeklődő hallgatók (MSc, PhD) bevonása a kutatói munkába.

Szemináriumunk 2017-től felvette a Farkas Miklós Alkalmazott Analízis Szeminárium nevet. Ezzel szeretnénk emléket állítani egyetemünk egykori tanszékvezető matematikaprofesszorának, aki elindította egyetemünkön a matematikus-mérnök képzést, és a stabilitáselmélet valamint a biomatematika terén elért jelentős tudományos eredményeivel ill. könyveivel nagyban hozzájárult az alkalmazott matematika erősödéséhez. (English version of the introduction.)

From the autumn semester of 2017 the talks will be in English on a regular basis. / 2017. őszi félévétől az előadásokat angol nyelven tartjuk.

Organizers / Szervezők: Faragó István1,2,3, Karátson János1,2,3 ,Horváth Róbert1,3 ,Mincsovics Miklós1,3 (1BME, 2ELTE, 3MTA-ELTE NUMNET)

Request for e-mail notifications and remarks to the organizers / Feliratkozás az e-mail listára ill. egyéb megjegyzések a szeminárium szervezőihez

Prospective speakers:
26 September:  Éva Gyurkovics
3 October: Zahari Zlatev
10 October: Tamás Kalmár-Nagy
17 October: László Székelyhidi
24 October: Svetozar Margenov

Next seminar:

26 September (Thursday) 2019, 10:15, H306 (BME, building H)

Éva Gyurkovics (BME, Department of Differential Equations)

Stability and stabilization with applications

In this talk, a short survey will be given about the results of the last three years achieved by several colleagues. Firstly, the stability analysis of continuous- and discrete-time time-delay systems based on a set of Lyapunov–Krasovskii functionals (LKFs) will be discussed. An important task in this problem is the estimation of the derivatives and differences of the LKFs. To this end, new multiple integral and summation inequalities will be presented that involve several famous inequalities known before. It will be shown that the proposed set of sufficient stability conditions given by LMIs can be arranged into a bidirectional hierarchy establishing a rigorous theoretical basis for comparison of conservatism of the investigated methods. Sufficient stability conditions will also be presented for the case of time-varying delays based on a parameterized family of LKFs involving multiple integral terms. Comparisons of several bounding inequalities proposed recently for the estimation of integrals and sums of quadratic functions will be discussed: the equivalences of several known variants of the free matrix based inequalities and their generalized and simplified forms are shown. Then, the relationship between the (simplified) free matrix based inequality and the combination of the Bessel-based inequality with different bounding inequalities affine in the length of the intervals are investigated.

Secondly, the results are applied to the non-fragile exponential synchronization problem of complex dynamical networks with time-varying coupling delays via sampled-data static output-feedback controller involving a constant signal transmission delay.

Finally, an algorithm terminating in finitely many steps will be given to determine the dynamic output feedback control with suboptimal finite-frequency H norm bound. Two case studies will be presented to illustrate the effectiveness of the proposed method.

Previous seminars

19 September 2019

Yiannis Hadjimichael (NUMNET MTA-ELTE research group)

High order discretization methods for spatial dependent SIR models

In this talk, an SIR model with spatial dependence is discussed and results regarding its stability and numerical approximation are presented. SIR models have been used to describe epidemic propagation phenomena, and one of the first models is derived by Kermack and McKendrick in 1927. In such models, the population is spit into three classes: $S$ is the group of species susceptible to infection, $I$ is the compartment of the ill species, and $R$ the class in of recovered species. We consider a generalization of the original Kermack and McKendrick model in which the size of the populations differs in space. The use of local spatial dependence yields a system of integro-differential equations. The uniqueness and qualitatively properties of the continuous model are analyzed. Furthermore, different choices of spatial and temporal discretizations are deployed, and step-size restrictions for population conservation, positivity and monotonicity preservation of the discrete model are investigated. We provide sufficient conditions under which high order numerical schemes preserve the discrete properties of the model. Computational experiments verify the convergence and accuracy of the numerical methods.

Presentations in 2018/192017/182016/17