Hooman Fatoorehchi Assistant Professor School of Chemical Engineering University of Tehran, Tehran, Iran Formulas in this page are typed in $\LaTeX$. Process Control Linearization of a Nonlinear Multivariate Function: $\Large f(x,y,z) \approx f(x_0,y_0,z_0) + \frac{\partial f}{\partial x} \Bigr\rvert_{x = x_0} (x-x_0) + \frac{\partial f}{\partial y} \Bigr\rvert_{y = y_0} (y-y_0) + \frac{\partial f}{\partial z} \Bigr\rvert_{z = z_0} (z-z_0). $ Definition: A continous time system is said to be causal if it produces a response y(t) only after the application of excitation x(t). That means for a causal system the response does not begin before the application of the input x(t). Definition: A linear, time-invariant system is said to be minimum-phase if the system and its inverse are causal and stable. BIBO Stability Theorem: A linear control system is stable if all the roots of its characteristic equation locate in the LHP (left half plane in the complex plane). Hint: The characteristic equation can be obtained by setting the denominator of the closed-loop transfer function to zero. My Notes on the Laplace Transforms [pdf file] [tex file] Root Locus Bode Diagrams [in Farsi]