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Hi everyone my name is Claire Tomlin Iamp;#39;m a professor of electrical engineering and computer sciences at UC Berkeley and this is the 19th module in a series of modules that we are recording to support the course eecs 221 a linear system theory at Berkeley in this module weamp;#39;re going to be discussing the solution to the linear time varying system and if we recall in the last module we presented a piece of that solution we presented the state transition matrix so letamp;#39;s just recall what the state transition matrix is itamp;#39;s given as the solution to the following matrix differential equation X dot of T is equal to a of T X of T weamp;#39;re now in this case in this matrix differential equation X of T is a matrix so itamp;#39;s a matrix in our n by N and of course a of T is our n by n matrix so the solution to that differential equation starting at an initial condition which is the identity is defined as the state transition matrix and we recall that we use the
