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Unformatted text preview: System State and Differential Equations EE 313 Linear Systems and Signals Spring 2009 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin 3  2 f y a y a y a y = + + + 1 2 y x y x y x = = = 3 2 1 ( 29 ( 29 ( 29 f x a x a x a x y x x y x x y + = = = 3 2 2 1 1 3 3 2 2 1 System State • Example: Reformulate N thorder differential equation into N simultaneous firstorder differential equations • Define three state variables • After substituting the state variables, we obtain a statespace description as Lathi, 2 nd ed, Section 1.10 3  3 f x x x a a a x x x +  = 1 1 1 3 2 1 2 1 3 2 1 f b x A x + = System State • By putting the state variables in vector x , • If A is not a function of time, then solution is – exp( M ) for matrix M yields a matrix dt t f e e t t t ∫ + = ) ( ) ( ) ( b x x A A 3  4 System State • General form of statespace description • Statespace descriptions can – Describe timevarying and nonlinear systems – Be simulated by computer (e.g. Spice for circuit simulation) • Knowledge of state variables allows one to determine every possible output of the system • Statespace descriptions covered in controls courses, e.g. EE 362K Intro. to Automatic Control f b x A x + = 3  5 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 t f b...
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This note was uploaded on 01/22/2012 for the course EE 302 taught by Professor Mccann during the Spring '06 term at University of Texas.
 Spring '06
 MCCANN

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