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in this video we will discuss how we can determine whether or not a system is stable by looking at the pole locations of the transfer function H of s so to begin lets think a little bit about poles and this is a somewhat of a review of the pole-zero plot video a pole that is to the right of the imaginary axis in the complex plane so the one Ive drawn here corresponds to an increasing exponential complex poles also correspond to exponentially increasing sinusoidal that Im shading in corresponds to a time signal that increases without bound now we know from our previous discussions of stability that a system is stable if for a bounded input the output is bounded so how can we look at that in terms of pole locations to determine whether or not a system is stable well it turns out to be quite simple youll recall that the output of a system Y is the transfer function times the Laplace transform of the input and stability means that if X of T is bounded so the magnitude of X of T is les