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Unformatted text preview: 8  1 Review Session for Week 8 Scott Hsieh, Stanford 2011.05.22.06 Review Session 8 Autonomous linear dynamical systems as problem setup Review of solution techniques Practice problems 8  2 Review Session for Week 8 Scott Hsieh, Stanford 2011.05.22.06 The Autonomous LDS The fundamental description of the autonomous LDS in discrete time is x ( t + 1) = Ax ( t ) By iterating, solutions are of the form x ( t ) = A t x (0) In continous time, we have: x ( t ) = Ax ( t ) We know from lecture that solutions are of the form x ( t ) = e At x (0) An alternative (engineering) approach to thinking about the continuoustime problem is to discretize the problem into small time intervals. Using the definition of the derivative, we have for very small t that x ( N t ) = (1 + A t ) N x (0) 8  3 Review Session for Week 8 Scott Hsieh, Stanford 2011.05.22.06 The Matrix Exponential For these two solutions to be consistent, we need that e A = lim k (1 + A/k ) k (This matches the most common definition of...
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This note was uploaded on 08/06/2011 for the course EE 263 taught by Professor Boyd,s during the Summer '08 term at Stanford.
 Summer '08
 BOYD,S

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