discrete−time systems and the z transform
Adaptive control and neural network control of nonlinear discrete time systems
... followings: φ(W, z) = W T S (z) W, S (z) ∈ Rl S (z) = [s1 (z) , s2 (z) , , sl (z) ]T , (2.8) [s(zj )]dj (i) , (2.9) si (z) = i = 1, 2, , l j∈Ii where z ∈ z ⊂ Rm is the input to HONN, l the NN nodes ... ∗ T S (z) + where W ∗ is ideal constant weights, and z z, z ∈ z (2.14) is the approximation error ¯ ¯ Lemma 2.10 [1] For the Gaussin RBFNN, if z = z − ψ where ψ is a bounded vector ˆ and constant ... stability theory and the progress of control theory improved the understanding of adaptive control and by the early 1980’s, several adaptive approaches have been proven to provide stable operation and...
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The z-Transform
... replace: r and T , with z This produces the standard form of the ztransform: EQUATION 33-1 The z- transform The z- transform defines the relationship between the time domain signal, x [n] , and the z- domain ... as poles and zeros This provides the second general form of the z- domain: EQUATION 33-4 Transfer function in pole-zero form H [z ] ' (z & z 1) (z & z 2) (z & z 3)þ (z & p 1) (z & p 2) (z & p 3)þ ... i.e., z, z 2, z 3, þ By multiplying both the numerator and denominator of our example by z , we obtain: H [z] ' 0.389 z & 1.55 8z % 2.338 z & 1.55 8z % 0.389 z & 2.161 z % 2.03 3z & 0.878 z % 0.161...
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Tài liệu ADVANCES IN DISCRETE TIME SYSTEMS docx
... (k )z( k) Also, the controlled output z may be expressed as z = T zw0 (z) w0 where,T zw0 (z) = AK B0 CK (18) If w0 is white noise with indensity matrix I and the closed-loop sys‐ tems is stable then ... subject to T zw w∈L 2+ ∞ and Z with appropriate dimensions, we have X T Z + Z T X + X T YX ≥ − Z T Y −1 Z 3.2 Robust admissibility analysis The following two theorems give a necessary and sufficient condition for the...
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Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension
... discovery of the light bulb and the electric motor In the mid-1940s, when the nuclear force was harnessed, the world was again t u r n e d upside down with the development of the atomic and hydrogen ... the universe is the realization that higher-dimensional geometry may be the ultimate source of unity in the universe Simply put, the matter in the universe a n d the forces that hold it together, ... n puzzled as to why the basic forces that hold together the cosmos—gravity, electromagnetism, a n d the strong a n d weak nuclear forces—differ so greatly Attempts by the greatest minds of the...
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Lean Manufacturing and the Environment: Research on Advanced Manufacturing Systems and the Environment and Recommendations for Leveraging Better Environmental Performance doc
... using the new standard, it found that one fully met the standard, and the second barely missed meeting the standard due to formaldehyde off-gassing The company worked to address the off-gassing and ... in recent years document the competitive pressures arising from globalization and other factors See: Thomas Friedman., The Lexus and the Olive Tree: Understanding Globalization (Thorndike, ME: ... that the improvements from the kaizen “blitz” are sustained over time Kaizen can be used as an implementation tool for most of the other lean methods 5S 5S is a system to reduce waste and optimize...
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Regional Food Hub Resource Guide: Food hub impacts on regional food systems, and the resources available to support their growth and development pdf
... and they all share the following attributes: Types of Services/Activities Offered by Regional Food Hubs Operational Services zz zz zz zz zz zz zz Distribution Aggregation Brokering Branding and ... market promotion Packaging and repacking Light processing (trimming, cutting, and freezing) Product storage Producer Services zz zz zz zz zz zz zz Actively linking producers and buyers Transportation, ... Community/ Environmental Services zz zz zz zz zz zz zz zz Increasing community awareness of “buy local” benefits Distributing to nearby food deserts7 Food bank donations Youth and community employment...
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Comparison between the Matrix Pencil Method and the Fourier Transform Technique for High-Resolution Spectral Estimation
... will be utilized in making a comparison between the Matrix Pencil Method and the Fourier Transform Technique z0 z* L z1 иии zL 01 zL 01 z *01 иии L * z2 z* ͬ * z L 01 иии * z1 zL z* ͬ (3.4) (3.5) ... as z T Å [zj , zj/1 , , zN0L/j01 ]; j j Å 0, , L (3.3) The new Z0 f b and Z1 f b are better conditioned [2, Appendix B] than Z0 and Z1 , which are formed for the ordinary MPM; that is, Z0 f ... Z1 f b2 (N0L ) 1L Å ͫ z1 z2 иии zL 01 * z L 01 z *02 иии L * z1 zL z* ͬ , (3.2) where * denotes complex conjugate, L is called the pencil parameter, and the transpose of zj ( j Å 0,...
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visions of awakening space and time dogen and the lotus sutra may 2007
... religio-philosophical theories: the more a theory leads us to recognize the microcosmic and cosmic dimensions of reality, the more true the theory.’’10 Thus the performance of the mantra or Dharmic ... performance, and they follow their emergence with ritual offerings to the Buddha Also, the Lotus Sutra emphasizes ritualized recitation of itself The fourth aspect of the sacred is the role of nature and ... expressions of the teaching and its meaning, rather than as means to discover and attain some understanding of it Therefore, the strong emphasis in much of Zen training is the mindful and dedicated...
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selfless insight zen and the meditative transformations of consciousness mar 2009
... in the certainty that they occupied the very center of the whole universe All other planets had seemed to revolve around them, as did the Sun itself! (Of course, in ignorance and arrogance, they ... in this series: Zen and the Brain [ZB: ] and Zen-Brain Reflections [ZBR: ] Zen is no simple topic Neither is the brain In my role as a secular guide to the ways these two topics are interrelated, ... pursuing them into the research laboratory I began Zen training late During these last three decades, I have been learning how to handle a sword poised at the cutting edge of both Zen and the neurosciences...
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Discrete Time Systems Part 1 pdf
... is the gate size; and z( k) is the observation at time k The parameters MN, n, m , and GS determine the implementation complexity and performance of the DF The number of possible values of the ... satisfy the constraints imposed on state estimates, are determined and the other initial quantization levels are discarded If the number of admissible initial quantization levels is zero, then the ... particles and the DF for which the random variables x (0) and w(k) were approximated by the approximate random variables with possible values (which are given in Section 3); the gate size (GS) and...
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Discrete Time Systems Part 2 potx
... B, C, H and Hd are of appropriate dimensions The function f : R s1 × R s2 → R q satisfies the Lipschitz condition with Lipschitz constant γ f , i.e : ˆ z1 − z1 ˆ ˆ ˆ ˆ , ∀ z1 , z2 , z1 , z2 ≤ γf ... ˆ ˆ ˆ ˆ , ∀ z1 , z2 , z1 , z2 ≤ γf (2) f z1 , z2 − f z1 , z2 ˆ z2 − z2 Now, consider the following new structure of the proposed observer defined by the equations (78) : ˆ ˆ ˆ x ( k + 1) = A ... and therefore the estimation error is asymptotically stable This ends the proof of Theorem 2.1 Remark 2.2 The Schur lemma and its application in the proof of Theorem 2.1 are detailed in the Appendix...
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Discrete Time Systems Part 3 ppt
... (1995) and Darouach; Zasadzinski & Keller (1992)), Chang and Hsu (Chang & Hsu (1993)) and Hou and Müller (Hou & Müller (1993)) They utilized some transformations to make the original systems ... ˆ ˆ ˆ ˆ xk/t+1 and xk/k respectively reduce to xk/t and xk/k−1 which are respectively the optimal smoother and the optimal filter obtained from the standard Kalman filter Then, the above equality ... for the state-space model which explicitly contains the unknown inputs We can indicate that the algorithm has a rather simple form and also has consistency with both the Kalman filter and the standard...
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Discrete Time Systems Part 4 pptx
... Discrete Time Systems Time Systems where xk ∈ R nx is the state vector, yk ∈ R ny stands for the output vector and wk ∈ R nx and vk ∈ R ny are the output and measurement noises respectively The uncertainties ... company and the environmental cost for the planet Another application is based on the knowledge of the position and velocities of cell phones in a network, allowing an improved handover process (the ... denotes the expectation operator, cov {•} stands for the covariance, Z † represents the pseudo-inverse of the matrix Z, diag {•} stands for a block-diagonal matrix Uncertain system modeling The following...
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Discrete Time Systems Part 5 potx
... D( z) = zE − A , furthermore, zE − As is shown as −1 zE − As = T ( z) Dm ( z) Q( z) N ( z) N r D −1 −1 ( z) and V ( z ) is the zeros polynomial of C [ zE − A] B = N ( z) / D( z) = U −1 ( z) V ( z) ... decomposition), U ( z) = D( z) , that is, N ( z) = D − ( z) V ( z ) So zE − As can be rewritten as −1 zE − As = N r −1 T ( z) Dm ( z) Q( z) V ( z) As T ( z) , Dm ( z) , Q( z) , V ( z) are all stable ... ( z) u( k ) + Dd ( z) R( z) N f ( z) f ( v( k )) + S( z) y( k ) − T ( z) N m ( z) rm ( z) The output error e( k ) is represented as following e( k ) = {[Dd ( z) R( z) N ( z) − Q( z) N r ]u( k ) + Q( z) N...
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Discrete Time Systems Part 6 pptx
... input w to the controlled output z is ⎡Tzw ( z) ⎤ ~ Tzw ( z) = ⎢ ˆ ˆ ˆ ⎥ Note that γ I − TzwTzw > is equivalent to ⎣ T0 ( z) ⎦ ~ γ I − TzwTzw > T0~T0 > for all w ∈ L2 [0, ∞ ) , and Tzw ( z) ∈ RH ... shows the comparison of Theorem and Theorem Some phenomenons (the solvability of Theorem and Theorem depends on the l and m When m > l, Theorem tends to have a higher solvability than Theorem And ... ∈ Rn×m Note that Z is ˜ ∈ and Z where ε is a given real scalar, Z = ˜ = [ z T , z T , · · · , z T ] T , where z T , ≤ constructed from Z with n rows drawing from Z, i.e., Z ˜ ˜ ˜ ˜ n i ˜ ˜ i...
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Discrete Time Systems Part 7 ppt
... Hence, we obtain another theorem below ˆ Theorem 6.1 Given integers dm and d M , and scalars ρi and ρi , i = 1, · · · , Then, (21) becomes an observer for the system (19) and (20) with ΔA = ΔAd ... e.g., [1~5] and the references therein) However, these solutions focused mainly on keeping stability of the faulty systems and in less consideration of other performance indices Actually, the performance ... information on the output and input In the following, we make analysis of the existence of observers Section 5.1 analyzes the observer of a nominal system, and Section 5.2 considers the robust observer...
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Discrete Time Systems Part 8 pot
... ≤k−n Z (k) − Z (l ) (7) such that Z (lk ) = [ z( lk − τmax ), , z( lk − τ ), , z( lk − τmin )] (8) Z (k) = Z (k) − Z (lk ) (9) and Then, if Z (k) is bounded we have Z (k) → as well as ν (z( k ... (3.3), and noting the fact lk ≤ k − n, there exist constants cz,1 , cz,2 , cs,1 and cs,2 such that Z (k − n ) ≤ cz,1 max{| y(k )|} + cz,2 k ≤k Δ s (k, n − 1) = (53) max { Z (k − n + k ) − Z (lk−n+k ... )) ≤ Z (k) , it is obvious that ν (z( k − τ )) − ν (z( lk − τ )) → as k → ∞ According to the definition of Z (k) in (9) and Assumption 3.1, we see that | ν (z( k − τ )) − ν (z( lk − τ ))| ≤ L ν Z (k))...
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Discrete Time Systems Part 9 ppt
... for the other agents, they are unaware of either the reference trajectory or the existence of the leader and the outputs of their neighbors are the only external information available for them, ... Coriolis-centripetal and the drag matrices, respectively and J is the matrix expressing the transformation from the inertial frame to the vehicle-fixed frame Moreover, g is the restoration force due to buoyancy and ... example, a capper in the casino lures the players to follow his action but at the same time he has to keep not recognized For another example, the plainclothes policeman can handle the crowd guide...
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Discrete Time Systems Part 10 pdf
... vertical and horizontal The simulated reference path ηr and the navigation path η are reproduced together by means of a visualization program (see a photogram in Fig 2) The units for the path ... for the advance and as well as for the descent/ascent along the path This rate will be referred to as the cruise velocity By the simulations, the adaptive control algorithm summarized in the ... where Mbn and Man are nominal values of Mb and Ma at the start point O, and MbΔ− , MbΔ+ ,MaΔ+ and MaΔ− are positive and negative variations at instants t A and t B on the points A and B of Fig...
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Discrete Time Systems Part 11 potx
... taken in the proof of Theorem are taken The main differences are related to i) the size and structure of the matrices and ii) the manipulations done to keep the convexity of the formulation ˜ Theorem ... 2)I p , the optimization variables W and Wd by K F and Kd F , respectively, using the definitions given by (10)–(11) and pre- and post-multiplying the resulting LMI by TH (on T the left) and by ... five zones, each of them with a thermocouple and a electric heater as indicated in Figure The state variables are the temperatures in each zone (x1 , , x5 ), measured by thermocouples, and the...
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