MIT6_241JS11_lec07

MIT6_241JS11_lec07 - 6.241 Dynamic Systems and Control Lecture 7 State-space Models Readings DDV Chapters 7,8 Emilio Frazzoli Aeronautics and

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Unformatted text preview: 6.241 Dynamic Systems and Control Lecture 7: State-space Models Readings: DDV, Chapters 7,8 Emilio Frazzoli Aeronautics and Astronautics Massachusetts Institute of Technology February 25, 2011 E. Frazzoli (MIT) Lecture 7: State-space Models Feb 25, 2011 1 / 11 Outline 1 State-space models E. Frazzoli (MIT) Lecture 7: State-space Models Feb 25, 2011 2 / 11 State of a system We know that, if a system is causal, in order to compute its output at a given time t , we need to know “only” the input signal over ( −∞ , t ]. (Similarly for DT systems.) This is a lot of information. Can we summarize it with something more manageable? Definition (state) The state x ( t 1 ) of a causal system at time t 1 is the information needed, together with the input u between times t 1 and t 2 , to uniquely predict the output at time t 2 , for all t 2 ≥ t 1 . In other words, the state of the system at a given time summarizes the whole history of the past inputs −∞ , for the purpose of predicting the output at future times. Usually, the state of a system is a vector in some Euclidean space R n . E. Frazzoli (MIT) Lecture 7: State-space Models Feb 25, 2011 3 / 11 Dimension of a system The choice of a state for a system is not unique (in fact, there are infinite choices, or realizations ). However, there are come choices of state which are preferable to others; in particular, we can look at “minimal” realizations....
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This note was uploaded on 01/12/2012 for the course ECE 6.241j taught by Professor Prof.emiliofrazzoli during the Spring '11 term at MIT.

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MIT6_241JS11_lec07 - 6.241 Dynamic Systems and Control Lecture 7 State-space Models Readings DDV Chapters 7,8 Emilio Frazzoli Aeronautics and

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