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Linear State Space Control Systems Solution Manual PDF Form

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[Music] looks like you guys are well on track and uh have already set a solid foundation for this topic the response of a state space equation we'll be talking about in general the response of x star equals to a x plus b u and we will talk about continuous time and discrete time cases let's start with the easy case if i want to solve x star if i want to solve a vector equation x star equals a x plus b u let's revisit what we can have for a scalar case x dot equals ax plus bu where these coefficients are all real and scalar here is the interesting observation that's key for this set of analysis imagine think about what we are doing here for this to work out this function x it must have the property if you take the derivative of the function it has the same very similar structure as the original function itself right what kind of function can have that property derivative is structurally the same as itself exponential function exponential function satisfies taking the derivative of e a t

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