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for the LQG Riccati equations g-B)DOTO B T2B2B (6.33) qY D B(B(B B -(g-B and for the Hoo(see(6. 17)-(6. 18))Riccati equations are comp ared, it is seen that the only difference is the additional terms I) B(Bf and I/t( in the upper right comer. Th LQG state feedback o o does not depend on B( i.e. how the disturb ances s'N. enter the system. Likewise, the Kalman gain o f in the LQG st ate estimator does not depend on T( i. e. all states are equally weighted. In contrast, o f in the Hoo st ate estimator depend on T( i.e. on the particular linear combination of st ates which corresponds to the output nNI One of the problems with the LQG compensator is, that even though LQ (full state informa- tion) has excellent guaranteed st ability margins (infinite gain margin and a phase margin of 00), it turns out that the observer based LQG compensator often is not very robust. The problem is, that some states often contribute more to the gain than others, but this can not compensated in the lQg Kalman filter as all st ates are weighted equally. In the Hoo st ate estimator, however, the designer can perform such weighting by virtue of the T( matrix and, hence, make the design more robust. Likewise, the dist urb ances s'N. can be weighted differently when computing the state feedb ack, and thereby the robustness of the sy stem can e improved Commercially available software now exists, which support the Hoo design problem, such as the MATLAB toolboxes [CS92, BDG 93]. Both toolboxes perform an iteration for I in order to find a near optimal Hoo compensator. 6.3.2 The Matlabtm toolbox es In addition to the Control Toolbox in MATLABTM, two toolboxes are available specifically for robust control design, i.e. robust control toolbox 6 Analy sis and Synthesis Toolbox. Both toolboxes are valuable pieces of software that provide a significant help in designing robust compensators in a smooth way, and they can both be recommended. Some of the advant ages of the 6 toolb ox are lent utility for converting a 2 x 2 block strukture into a st ate sp ace description Very natural functions for the ms, e.g. for interconnecting sy ster or closing loops(st arp. m) Good approach to 6, see Chapter 7. :;< . " #$))& #$)*& # #$%/&#$%0&& . 1 :;< ! : ! A :;< 2 :;< :; # & # $4Æ & :;< :;< A ! : ! 1 ! - ?-'9( 5,< 9)@ 5 - " . - $ ' 5 ' $ " 6 ! ! #& G # & < $ - /