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...ror prone. u(t) f(x(t), u(t), t) Figure 7. A conceptual block diagram for continuous-time systems. For example, a transfer function has zero-initial-state controllable canonical form (see for example =-=[8]): . x(t-=-) ∫ x(t) Ys ( ) s + b ----------- Us ( ) s 2 = ----------------------------- – a1s – a0 g(x(t), u(t), t) y(t) (2) 16 of 37s· x1 · which can be built as the composite actor shown in Figure 8. x...

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...analysis of the concept of state in the context of ant colony optimization can be found in [4]. A general analysis of the concept of state is given in the classical literature on linear system theory =-=[20]-=-, dynamic programming [2], and optimal control [3]. 3 For a discrete Markov decision process, the following holds by definition: P (x t+1 |x t , u t ) = P (x t+1 |x t , u t ), where x t = (x t , x t-1...

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...s a function of the state, as indeed stated by thesrst of the two properties. The denition of state given here is inspired by and is consistent with the classical denition given by Zadeh and Desoer [2=-=1-=-]. It is nonetheless a proper extension of that denition in the sense that we consider here systems for which the set of admissible inputs varies according to the preceding input-output history, while...

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...(t) such that the system (1) dx dt = Ax+BK(t)Cx, x ∈ Rn, is asymptotically stable. The problem of stabilizing system (1) with the help of a constant matrix K is classical for automatic control theory =-=[2, 3]-=-. From this point of view, Brockett’s problem can be reformulated as follows. To what extent are the possibilities of classical stabilization extended by introducing matrices K(t) that depend on time ...

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... Bayes Predictor for binary information. Markov Modelling Figure 7 Bayes Estimator and Predictor It has become conventional to introduce the abstract concept of a process through its statetransitions =-=[37]-=- rather than through the differential or difference equations which describe particular examples. To identify a real process on this basis, however, is not feasible, because the number of states is ge...

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...lem. For frequency-response problems an approach as in [17] may be more appropriate; it is not a-priori that poles play the same dominant role as in LTI. In earlier literature on LTV-systems, such as =-=[6]-=-, the system behavior shows characteristic polynomials with the Heaviside-operator as a variable and time functions as constants. Thus, the physical quality 'time' appears in two different ways. To ha...

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... advertisements at different nodes. Significantly, the formulation of BGP’s probabilistic dynamics as a linear system allows leveraging the body of work on stability analysis for linear systems (c.f. =-=[14]-=-). We demonstrate the utility of this model for several problems related to the analysis of the expected convergence behavior of BGP. The first problem we consider is that of determining whether a BGP...

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... is given by � ∞ L−{f(t)} = F(s) = f(t)e −st dt, (3) where the domain of integration fully includes the origin and any singularities occuring at that time. This form is adopted in many texts, such as =-=[8]-=-–[12]. The definition (3) of the Laplace transform implies the time-derivative rule 0 − L−{f ′ (t)} = sF(s) − f(0 − ), (4) whereby initial conditions existing before t = 0 are brought into the analysi...