Name: Anonymous 2008-03-30 23:32
Let A ∈ Rn and B ∈ R^n×m. Prove that if u(t) is a continuous
function, then the differential equation
dx/dt(t)= Ax(t)+ Bu(t),x(ti)= xi,t ≥ ti
has a unique solution x(·) in[ ti,+∞) given by
x(t)= (e^(t−ti)A)*xi + (e^tA)(I(ti to t)e^(−τABu(τ)) dτ)
I should just quit but I already have my degree :/
function, then the differential equation
dx/dt(t)= Ax(t)+ Bu(t),x(ti)= xi,t ≥ ti
has a unique solution x(·) in[ ti,+∞) given by
x(t)= (e^(t−ti)A)*xi + (e^tA)(I(ti to t)e^(−τABu(τ)) dτ)
I should just quit but I already have my degree :/