**Wednesday, 16:15 - 16:40 h, Room: H 2035**

**Radek Cibulka**

Quantitative stability of a generalized equation: Application to non-regular electrical circuits

**Coauthors: Samir Adly, Jiří V. Outrata**

**Abstract:**

Given matrices *B ∈ ***R**^{n× m}, *C ∈ ***R**^{m × n}, and mappings *f: ***R**^{n} → **R**^{n} , *F: ***R**^{m} rightarrows **R**^{m} with *m ≤ n*, consider the problem of finding for a vector *p ∈ ***R**^{n} the solution *z ∈ ***R**^{n} to the inclusion

\begin{equation} \label{eqIN}

p ∈ f(z) + B F (Cz).

\end{equation}

Denote by *Φ* the set-valued mapping from **R**^{n} into itself defined by

*Φ(z) = f(z) + BF(C z)* whenever *z ∈ ***R**^{n}. Our aim is to investigate stability properties such as Aubin continuity, calmness and isolated calmness of the solution mapping *Ψ:= Φ*^{-1}. Under appropriate assumptions, the verifiable conditions ensuring these properties are given in terms of the input data *f*, *F*, *B* and *C*. We illustrate our consideration on a particular examples arising from electronics.

Talk 3 of the invited session Wed.3.H 2035

**"Nonsmooth analysis with applications in engineering"** [...]

Cluster 24

**"Variational analysis"** [...]