Linearization of State Space Dynamics

[@javedakbar5375]

love you sir:::::::::::::::::: many many thanks . I'm doing masters but this is the first time I got the concept of linearization, Taylor series.. thank God I find your video.... lots of respect from Germany

[@卢俊杰-p7i]

35:35 the derivatives of x1 should be partial derivative of x2 multiply(x2-b) ,and the derivatives for x2 should be partial deriative ofx1 multiply(x1-a)

[@djtan775]

this lecture is very informative amazing !!!!

[@gabeitch7786]

Awesome lucture very useful

[@Zuwwar]

Very nice. However, I do have two different questions; 1). Why do we skip the first entry f(a) or f(b) of the Taylor Series while creating a Jacobian Matrix? Also, we are skipping the (x1-a) and (x2-b) term which are being multiplied with the partial derivatives in the Taylor Series. So, in short, why do we only consider the partial derivatives and skip the rest of the terms while filling the Jacobian? 2). My second question is; how is it possible that if I start from any non zero initial condition and somehow after some time my system reaches an equilibrium point xo, then my system will be stuck at the state forever? Because at that particular equilibrium point, my derivates and dynamics go to zero, so will I get a steady state after reaching xo? If yes, then what about a function lets say f(x) = cos (x) which has multiple operating or equilibrium points as you said in part 2 of this lecture? Cos(x) has multiple equilibrium points, you get one and then the other and so on - so after one equilibrium point our system or the dynamics of our system doesn't get stuck at that point forever but in fact it moves to the next equilibrium point.

[@emmanuelsheshi961]

excellent