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# lec9_print - Forced Dynamics of a Linear System Srinivas...

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Forced Dynamics of a Linear System Srinivas Palanki University of South Alabama Srinivas Palanki (USA) Forced Dynamics of a Linear System 1 / 12

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Dynamics of a Linear System A linear dynamical system in deviation form is represented as dX dt = AX + BU X (0) = X 0 (1) where X = x - x s U = u - u s (2) Srinivas Palanki (USA) Forced Dynamics of a Linear System 2 / 12
Dynamics of a Linear System We saw in the previous lecture that the solution of the above diﬀerential equation is given by X ( t ) = e At . X (0) + e At . Z t 0 e - At BU ( t ) dt (3) It is clear from the above equation that X ( t ) is aﬀected by: the initial conditions, X (0) the input vector, U ( t ) In the previous lecture, we studied the eﬀect of initial conditions (unforced response). We now study the eﬀect of the input (forced response). Srinivas Palanki (USA) Forced Dynamics of a Linear System 3 / 12

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Dynamics of a Linear System Forced Dynamics Consider the system represented by eq. (1) in the previous slide. Suppose that:
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## This note was uploaded on 01/07/2011 for the course CHE 452 taught by Professor Dr.srinivaspalanki during the Spring '10 term at S. Alabama.

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lec9_print - Forced Dynamics of a Linear System Srinivas...

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