MEEN 651 Control System Design Homework 9: Controllability/ObservabilityAssigned:Tuesday, 28 Oct. 2008 Due:Tuesday, 4 Nov. 2008, 5:00 pm Do the following problem from “Feedback Control of Dynamic Systems” 5thed., Franklin and Powell. Problem 1) Problem 7.5 Problem 2) Problem 7.6 Problem 3) Problem 7.14 (by hand, do not use Matlab) Problem 4) Problem 7.26 Do the following problems: Problem 5) We use the notation A > 0to denote a positive definite matrix (i.e. symmetric matrix with all positive eigenvalues), and A ≥0to denote a positive semi-definite matrix (i.e. symmetric with all eigenvalues greater than or equal to zero). Let Aand Bbe two n x nreal matrices which are positive definite. Show that A ≥Bif and only if B-1 ≥A-1. Problem 6) Is the system below controllable? Observable? ( )( )( )( )( )txtytutxtx101000110120100010=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡+⎥⎥⎥⎦⎤⎢⎢⎢⎣
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DYNAMIC SYSTEMS, positive definite matrix, controllable state space