Sifat-sifat sistem linear time varying

BUDHAYANTI, Clara Ika Sari, Dr. Ari Suparwanto, MSi

2003 | Tesis | S2 Matematika

Secara umum analisa sistem terdiri dari dua bagian : analisa kuantitatif dan kualitatif. Analisa kuantitatif mempelajari penyelesaian sistem dengan syarat awal dan fungsi input tertentu. Penyelesaian sistem ini ditentukan oleh matrik transisi dari sistem tersebut. Jika Φ(t,to) matrik transisi dari sistem linear time varying dan Φa(t,to) matrik transisi dari sistem dualnya maka Φa(t,to) = Φ*(to,t). Sedangkan analisa kualitatif mempelajari sifat-sifat umum dari sistem yaitu keterkendalian , keterobservasian dan kestabilan. Sistem linear time-varying terkendali pada to jika dan hanya jika sistem dualnya terobservasi pada to. Jika matrik B(⋅) dan C(⋅) dari sistem linear time varying terbatas pada (-∞,∞) dan state nol dari sistem linear stabil seragam secara asimtotik maka zero-state response stabil BIBO. Jika sistem linear time-varying stabil total maka zero-state response stabil BIB

System analyses generally consist of two parts : quantitative and qualitative. In the quantitative analyse we are interested in the exact response of system to certain input and initial conditions. Solutions of linear system are stated in terms of the state transition matrix . If Φ(t,to) transition matrix of linear system time varying and Φa(t,to) transition matrix of dual system then Φa(t,to) = Φ*(to,t). In the qualitative analyse we are interested in the general properties of a system such as controllability, observability and stability. Linear system time varying controllable if and only if the system observable. If the matrices B(⋅) dan C(⋅) of linear system time varying are bounded on (-∞,∞) then the uniformly asymptotic stability of the zero state implies the BIBO stability of the zero state response. Total stability implies BIBO stability

Kata Kunci : Sistem Linear Time Varying, Transition matriks, controllability, observability and stability