### Table 1 gives the declaration of the constituents in the coarse plant model of the landing gear. Using the above notation and the architectural breakdown in Figure 10, the closed loop system for the landing gear is represented by S P ^ C

1999

"... In PAGE 20: ...Type: Description xd : R ! R Plant state: door position (closed: 0, opened: 1) xg : R ! R Plant state: gear position (retracted: 0, extended: 1) d : R Plant parameter: door speed g : R Plant parameter: gear speed u11 : R ! f0; 1g Controller command: open door (hold: 0, open: 1) u12 : R ! f0; 1g Controller command: close door (hold: 0, close: 1) u21 : R ! f0; 1g Controller command: extend gear (hold: 0, extend: 1) u22 : R ! f0; 1g Controller command: retract gear (hold: 0, retract: 1) r : R ! f0; 1g Pilot command: extend gear (retract: 0, extend: 1) Table1 : Declaration of states and global variables. Proof: dP1e ^ (dP2e ; dP3e) ) fP-Alwaysg 2 (dP1e _ d e) ^ (dP2e ; dP3e) ) fAlways-introg ( 2 (dP1e _ d e) ^ dP2e) ; ( 2 (dP1e _ d e) ^ dP3e) ) fAlways-Once-Somewhereg ((dP1e _ d e) ^ dP2e) ; ((dP1e _ d e) ^ dP3e) ) fPLg ((dP1e ^ dP2e) _ (d e ^ dP2e)) ; ((dP1e ^ dP3e) _ (d e ^ dP3e)) ) fDefn, analysisg ((dP1e ^ dP2e) _ false) ; ((dP1e ^ dP3e) _ false)... ..."

Cited by 3

### Table 3: Reduced-order -stabilizing controllers for mass/spring systems. As the required closed-loop decay rate grows, the attainable controller order increases.

1997

Cited by 14

### lable there exists a state-feedback controller , u(t) = ?Kx(t), such that the poles (eigenvalues) of the closed-loop system can be located arbitrarily. State-space theory for feedback design was introduced by Kalman in the early sixties [10].Many text books are now available on this approach, see for example [9]. One state-space design theory, which is especially well suited for multivariable feedback systems, is the so-called linear-quadratic (LQ) theory. In the LQ theory the problem is to nd a state- feedback control law which minimizes an integral quadratic per- formance measure of the form

### Table 2: Closed-loop accuracy test

"... In PAGE 10: ...2 Closed-loop accuracy test Since the repeatability test gave good results, the closed loop accuracy test was performed on a single set of combined registration data. Table2 gives the values of Techo_frontal, Techo_axial, Tfrontal_axial thus obtained and compares Tfrontal_axial *Techo_frontal to Techo_axial. The homogeneous coordinates notation is used.... ..."

### Table 3.5: Closed loop properties in case of plant and controller configurations

### Table 2: GA Optimised Heading Controller Parameters Heading Controller Parameters 1st Heading Closed loop pole -0.0840

"... In PAGE 5: ... 4.3 Results After 100 generations of the GA, typical parameter values (see Table2 ) are obtained Table 2: GA Optimised Heading Controller Parameters Heading Controller Parameters 1st Heading Closed loop pole -0.0840... ..."

### Table 4.5: State-space Dimensions of Systems involved in the Design Process After closing the control loops sequentially, the closed-loop system T was analysed by means of norm calculations and in simulation. The controllers of the individual subsystems can be arranged in a compound system, as in Equation (4.19), that ts in

### Table VII. In this case, the performance output gain A2 shifts the control problem focus from mass 2 to the mass 3 position, so the importance of mass m3 uncertainty in the closed-loop system performance is emphasized.

### Table 3. Closed-loop Eigenvalues With Gain, 7149.

"... In PAGE 21: ... Nonzero eigenvalues of the symmetric part of 7149 are 485852495057 and 485856485153, which demonstrates that the symmetric part of 7149 is positive semidefinite. Closed-loop eigenvalues with this gain matrix are shown in Table3 . It should be observed that the gain matrix, 7149, successfully increased damping ratio of the first mode to 10 % without destabilizing other modes.... ..."

### Table 5. Closed-loop Eigenvalues With Gain, 7151.

"... In PAGE 22: ... (16) was 112 61 91049584859 49584859 049584859 048585754545259 049584859 49584859 049584859 48585355545093 which led to the cumulative gain matrix of 7151 for the third step with nonzero eigenvalues of the symmetric part at 485848575449 , 485850565251 , 485855485448 , 485857545752 , 495857575050 and 525850484849. Closed-loop eigenvalues with gain 7151 are shown in Table5 . Again, damping ratio in the first three modes has been increased exactly to 10 % as desired without destabilizing any other modes.... ..."