### 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 1 Methods for model order reduction of linear dynamic systems (after Antoulas and Sorensen (2001)).

2005

"... In PAGE 9: ... It is important that a reduced model preserves such properties of the original model as stability and passivity. There exists a large number of important results supporting these efforts; some examples are given in Table1 . The most advanced results here are established by control theory, which allows us to make the strong statement that model reduction of a linear dynamic system is solved in principle.... ..."

Cited by 1

### Table 1 Theories, systems and models discussed in this paper Classical decision theory

2002

"... In PAGE 3: ... However, this comparison gives some interesting insights into the relation among the areas, and these insights are a good starting point for further and more complete comparisons. A summary of the comparison is given in Table1 . In our comparison, some concepts can be mapped easily onto concepts of other theories and systems.... ..."

### Table 2: Initial Domain theory obtained from trained ANN for IEEE 14-bus system

"... In PAGE 4: ... (vii) With these 18 (3 bipolar inputs corresponding to each input data) inputs, a fully connected three-layered feed- forward MLP model (Rosenblatts, 1957) having 18 input neurons, 9 hidden neurons, and 5 output neurons, with semi-linear sigmoid activation function, is trained by Back Propagation (BP) [iterative, gradient, negative descent search, supervised] algorithm for five- class classification task so that line (MW) PI may be ranked in different levels according to their severity (Table 1). (viii) The rules extracted ( Table2 ) from a trained MLP model using large-weight algorithm are stored in a fuzzy rule base. (ix) Domain Knowledge (fuzzy rules extracted from MLP model) is integrated with the trained MLP model to select and rank the contingencies accurately and quickly.... ..."

### Table 1: Theories, systems and models discussed in this paper

2003

"... In PAGE 3: ... However, this comparison gives some interesting insights into the relation among the areas, and these insights are a good starting point for further and more complete comparisons. A summary of the comparison is given in Table1 . In our comparison, some concepts can be mapped easily onto concepts of other theories and systems.... ..."

Cited by 5

### Table 1. Theory Comparison

2005

"... In PAGE 7: ... Test Set Performance (results given as percentage) search to find most paths. The two systems do find different best clauses, as shown in Table1 which show both number of clauses and average clause length, including the head literal. Although most of the clauses found by Aleph are paths, the path finding implementation does find longer paths that are not considered by Aleph and also performs better on the training set.... ..."

Cited by 1

### Table 1. Characteristics of small amplitude internal waves from linear theory, and

"... In PAGE 4: ... #283#29 results in an eigenvalue problem which can be solved to give the dispersion relation for small-amplitude internal waves #28for example, see Gill #281982#29#29: ! 2 = N 2 k x 2 j ~ kj 2 = N 2 cos 2 #02: #284#29 The group velocity of the waves can be determined from this expression and therebyit can be shown that #02 represents the angle of propagation of the waves to the vertical. The polarization relations and other relevant properties of internal waves are listed in Table1 . For consistency with the results presented here, amplitudes of various #0Celds are given in terms of the amplitude A w of the vertical velocity #0Celd.... In PAGE 7: ... Although the incidentwavepacket may be stable to self-acceleration e#0Bects, the superimposed in- cident and re#0Dected waves are unstable if the amplitude of the incidentwave exceeds A w crit =2. That is, if A w #3EA w break = #10 2 ,1=2 sin #02 cos 2 #02 #11 N k x : #2811#29 Table1 summarises the #0Cnite-amplitude stability regimes described in sections 2. #28b#29 and #28c#29.... In PAGE 11: ... The wavepacket is of rela- tively small amplitude, A w =0:02N=k x . The #0Celd is normalised by the maximum initial value of huwi #28see Table1 #29. A horizontal dashed line is drawn to indicate the heightof the re#0Dection level #28the height where the Doppler-shifted frequency of the wave equals the buoyancy frequency N#29.... In PAGE 11: ... Figure 3b illustrates the structure of the re#0Dected waves at time t apos; 48T. The plot shows contours of the vertical displacement #0Celd, #18, normalised by the maximum value of this #0Celd at time t = 0 #28see Table1 #29. The hori-... In PAGE 22: ...s in Fig. 2, Fig. 11 shows time series of ,h#10#18i, computed for simulations of small- and large-amplitude horizontally compact wavepackets with a,d#29 k z = ,0:4k x , b,e#29 k z = ,0:7k x and c,f#29 k z = ,1:4k x . Each time series is normalised by the predicted maximum initial value of ,h#10#18i #28see Table1 #29. In the small-amplitude cases, the horizontally compact and periodic waves show sim- ilar behaviour.... ..."

### Table 2 Maximum throughput in the linear network. Theory Simulation

"... In PAGE 15: ... In particular, when the common ex- ogenous load value, , is increased, the leftmost node saturates rst, due to the cumulative e ect explained above. In Table2 , we show the maxi- mum throughput observed at nodes A1, A7 and A14 in the simulation as well as the theoretical predictions. 0 0.... ..."

### Table 1. BKYY-DR System and Theory

1997

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### Table 1 The classical geometers were able to give detailed descriptions of those solutions that satisfy additional conditions (e.g. solutions corresponding to surfaces of rota- tion), but there was no methodology at hand by which one could characterize the entire space, or at least a reasonably large subset thereof. A brief discussion of their results is relegated to the third section of this paper. The intervening period of time has seen the development of the theory of inte- grable systems, or soliton theory. The idea of this theory is to nd a bi-Hamiltonian

1994

"... In PAGE 6: ...) We remind the reader that proofs for the case that quot; is the Minkowski metric can be found in [21]. As noted in Table1 the soliton P.... In PAGE 6: ... A surface with a linear rela- tionship between the Gauss curvature K and the mean curvature H is called a linear Weingarten surface. Table1 gives a complete list, up to homothety and parallelism, of the nontrivial linear Weingarten surfaces. So far we have restricted ourselves to linear Weingarten surfaces in three-dimen- sional Euclidean space.... ..."

Cited by 7