Stability of Symmetric Hyperbolic Systems with Nonlinear Feedback

Autor:	Gideon Peyser
Rok vydání:	1975
Předmět:	Lyapunov function Applied Mathematics Operator (physics) Mathematical analysis Space (mathematics) Stability (probability) Instability Computational Mathematics symbols.namesake Nonlinear system Square-integrable function Distributed parameter system symbols Analysis Mathematics
Zdroj:	SIAM Journal on Mathematical Analysis. 6:925-936
ISSN:	1095-7154 0036-1410
DOI:	10.1137/0506081
Popis:	This paper studies the stability of distributed parameter systems represented by the symmetric hyperbolic system $\Phi_i + \sum _{i = 1}^m A_i \Phi_{x_i} + B\Phi = \mathcal{F}\Phi $, with the nonlinear feedback operator $\mathcal{F}$. The trajectory solution is derived, with the system states as elements in the space of square integrable functions. Stability and instability criteria are obtained for the trajectory solutions. Also, global and local asymptotic and $L_2$-stability criteria, and analogues of Lyapunov’s first method are derived.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4cdd37f2c0b8d3a27392d520875c8ef9 https://doi.org/10.1137/0506081 Zobrazit plný text záznamu