By Cornelius Thomas Leondes
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Those lawsuits comprise lectures given on the N. A. T. O. complicated examine Institute entitled "Scattering idea in arithmetic and Physics" held in Denver, Colorado, June 11-29, 1973. we now have assembled the most sequence of lectures and a few offered by means of different individuals that appeared clearly to enrich them.
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Extra resources for Control and dynamic systems : advances in theory and applications. Vol. 9
Z. y. 29) where zi is the output of the minimalorder observer and y. is the plant output vector. Applying the control law u. = K. x. with the state estimate x. of Eq. 29) -1 1-1 —1 29 LESLIE M. NOVAK gives the closed-loop state equation c. _ (A. )x. z. 30) Also applying the same input to the observer gives K )P z T. (A. + BiKi)V1Rixi. 31) Zi+1 - Ti+1(Ai + Bi i i i + Combining Eqs. R. 3 ) z —i The stability properties of the overall closed-loop system become apparent when the system is viewed in a different state space.
0 for all "i". This important special -1 case is considered next. Rather loosely stated, in the absence of measurement noise, "m" of the system states are known exactly and it is only necessary to estimate the remaining "n -m" states.
13), = Ki+1 . 15) into the observer system defined by Eq. 9) gives the result Z. Z. 16) LESLIE M. NOVAK structure to the Kalman filter. If K 1+1 is taken to be the Kalman filter gain matrix, the observer obtained is identical to the Kalman filter. If the designer picks the gain matrix K i+1 according to some other criterion, the observer then may be viewed as a suboptimal Kalman filter. ) Therefore, a Kalman filter is an n-dimensional observer for which the weighting matrix Di+l has been chosen to minimize the mean square estimation error.