Teorema Lyapunov pada sistem Singular

SOLIKHATUN, Dr. Ari Suparwanto, M.Si

2005 | Tesis | S2 Matematika

Teorema Lyapunov dapat digunakan untuk mengkarakterisasi kestabilan sistem singular. Ada dua perumuman persamaan Lyapunov yang terkenal yaitu diperkenalkan oleh Lewis dan Takaba. Perumuman persamaan Lyapunov yang diperkenalkan oleh Lewis mengarah pada kesimpulan yang tidak benar tentang kestabilan. Kemudian perumuman persamaan Lyapunov tersebut akan diperbaiki, yang serupa dengan persamaan Lyapunov asli. Perumuman persamaan Lyapunov yang dihasilkan ekuivalen dengan perumuman persamaan Lyapunov yang diperkenalkan oleh Takaba.

The Lyapunov theorem can be used to characterize stability for singular systems. There are two well-known generalized Lyapunov equations that were proposed by Lewis and by Takaba. Generalized Lyapunov equation were proposed by Lewis lead to incorrect conclusion about stability. Then, it will be repaired which the generalized Lyapunov equation is similar to the original. The result of generalized Lyapunov equation is equivalent to the generalized Lyapunov equation were proposed by Takaba

Kata Kunci : Sistem Singular, Persamaan Lyapunov, Lyapunov equation, singular systems, regular, stability, impulse free, observability, impulse observability, detectability, matrix, positive definite.