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International audience; In this paper, the algebraic analysis approach to linear state-space systems is further developed using rings of integro-differential operators. The module structure of linear state-space systems is investigated over these rings. The module associated with a linear state-space system is shown to be the direct sum of the stably free module defined by the linear system without inputs and the free module defined by the inputs of the system.

This article is concerned with the robust convergence analysis of iterative learning control (ILC) against nonrepetitive uncertainties, where the contradiction between convergence conditions for the output tracking error and the input signal (or error) is addressed. A system equivalence transformation (SET) is proposed for robust ILC such that given any desired reference trajectories, the output tracking problems for general nonsquare multi-input, multi-output (MIMO) systems can be equivalently transformed into those for the specific class of square MIMO systems with the same input and output numbers. As a benefit of SET, a unified condition is only needed to guarantee both the uniform boundedness of all system signals and the robust convergence of the output tracking error, which avoids causing the condition contradiction problem in implementing the double-dynamics analysis approach to ILC. Simulation examples are included to demonstrate the validity of our established robust ILC results.

In this paper we present new methods for the reduction of a polynomial system matrix describing a discrete linear repetitive process, to equivalent singular and non-singular 2-D state space representations. Particularly, a zero coprime system equivalence transformation resulting in a singular Roesser state space model, preserving the core algebraic structure of the original system matrix, is proposed. As a second step utilizing the singular Roesser model introduced, we further reduce the system to a non-singular, zero coprime system equivalent Roesser model. Both models are constructed by inspection or by applying elementary matrix manipulations and have significantly smaller dimensions compared to similar reductions found in the literature.

The stabilization problem for the Schrodinger equation with an input time delay is considered from the view of system equivalence. First, a linear transform from the original system into an exponentially stable system with arbitrary decay rate, also called “target system”, is introduced. The linear transform is constructed via a kind of Volterra-type integration with singular kernels functions. As a result, a feedback control law for the original system is obtained. Secondly, a linear transform from the target system into the original closed-loop system is derived. Finally, the exponential stability with arbitrary decay rate of the closed-loop system is obtained through the established equivalence between the original closed-loop system and the target one. The authors conclude this work with some numerical simulations giving support to the results obtained in this paper.

This paper develops a direct method for transforming a polynomial system matrix describing a discrete wave linear repetitive process to a 2-D singular state-space Roesser model description where all relevant properties, including the zero coprimeness properties of the system matrix, are retained. It is shown that the transformation is zero coprime system equivalence. The structure of the resulting system matrix in singular form and the transformation are also established.

We propose that it is an important ongoing research agenda to devise a new classification of economic systems based on empirical observation rather than abstract reasoning, and then subject this to the test of empirical validity by exploring whether this taxonomy explains observed behaviour. However, we do not ourselves yet attempt a new classification of economic systems; rather, we draw on the Varieties of Institutional Systems configuration (Fainshmidt, Judge, Aguilera and Smith, 2018) as the basis for our empirical work. We ask whether, holding country-specific institutional factors, sector-specific technological characteristics and ownership-specific firm-level attributes constant, enterprise performance is contingent on the configuration. We test this idea on the World Bank Enterprise Survey of 30,000 firms in more than 57 countries between 2006 and 2016, using a production function methodology. Our proposition that taxonomic systems matter is supported by the evidence. We find that in these understudied economies, systems based on both free market logic and state capitalism achieve equivalent firm-level performance, while systems allowing rent-seeking and cronyism are less efficient. Thus, this new approach allows for system equivalence (equifinality) as well as system superiority.

Equivalence checking (EC) is a crucial component of integrated circuit (IC) design. EC problem has become even more challenging with the ever-worsening process variations. In our earlier work [10] , we researched optimization-based analog equivalence checking (AEC) between Simulink and HSpice models, where we proposed a methodology to find a boundary of equivalence. Although the significance of the effect of process variations is widely accepted, there is limited number of studies addressing the impact of process variations on AEC. In this study, we propose a novel technique to incorporate process variations in AEC. We build a multi-objective optimization problem utilizing evolutionary computation. In this problem, we search for the boundary of equivalence both considering the equivalence value resulting from the effect of process variations and closeness to the boundary. In process variations-effect analysis, we utilize Quasi Monte Carlo (QMC) method to generate samples, which makes it possible to estimate the yield with fewer samples compared to Monte Carlo (MC) method. We generate process variations-aware equivalence boundaries for different equivalence values. We validated our analysis on three designs, an inverter, an operational amplifier, and a buck converter. Our approach proved to be a credible tool for investigating the effect of process variations on the equivalence boundary.

Objective: Invasive coronary angiography remains the cornerstone for evaluation of coronary stenoses despite there being a poor correlation between luminal loss assessment by coronary luminography and myocardial ischemia. This is especially true for coronary lesions deemed moderate by visual assessment. Coronary pressure-derived fractional flow reserve (FFR) has emerged as the gold standard for the evaluation of hemodynamic significance of coronary artery stenosis, which is cost effective and leads to improved patient outcomes. There are, however, several limitations to the use of FFR including the evaluation of serial stenoses. Method: In this article, we discuss the electronic-hydraulic analogy and the utility of simple electrical modelling to mimic the coronary circulation and coronary stenoses. We exemplify the effect of tandem coronary lesions on the FFR by modelling of a patient with sequential disease segments and complex anatomy. Results: We believe that such computational modelling can serve as a powerful educational tool to help clinicians better understand the complexity of coronary hemodynamics and improve patient care.

Modern electric power systems are characterized by a very complex structure of electrical connection circuits and a huge number of elements (stations, loads, synchronous compensators, etc.). Difficulties of calculations at the occurrence of large disturbances and analysis of the obtained results quickly increase with the increase of the number of elements of power systems, which cause in steady and transient modes various phenomena and accompanying processes, which cannot be analyzed without taking various kinds of equivalence. Therefore, it is generally advantageous to simplify power grid schemes in a stability analysis. In action, it is sought to obtain a scheme that reduces the number of elements involved, but at the same time allows for sufficiently reliable and practically foreseeable results. Because the problem of building models that best reflect actual processes is always relevant. This article deals with the proposal for system equivalence in relation to the Electrical power system (EPS) of the Kyrgyz Republic (KR).

This paper considers the output regulation problem of linear singular multi-agent systems by using both state feedback control and time-delay feedback control. Sufficient conditions for the output regulation problem of singular multi-agent systems are proposed by adopting restricted system equivalence properties under the state feedback control strategy. A reduced-order normal system is obtained by a standard coordinate transformation. It is shown that state feedback control can solve the output regulation problem of the reduced-order normal systems and the original singular multi-agent systems. Numerical examples are presented to illustrate the effectiveness of the proposed method.

In the last decades the LPV modelling paradigm grew up from the desire of having a gain scheduling method with guaranteed stability and performance bound by using as much as possible from the classical design techniques. LPV design becomes a proven method of the field of robust control through a series of applications. While system equivalence, state transformation and loop transformation are fundamental concepts and efficient tools of the linear time invariant (LTI) theory, in the context of the LPV framework some basic modelling issues still evades the attention of the researchers. The main goal of the paper is to provide an initialization in LPV modelling and to review the fundamental concepts in order to eliminate the possible pitfalls that often occur in the related literature. The work provides an opportunity for pointing out some research topics that might be interesting for a much larger audience, too.

The so-called lumped disturbance in this paper includes modeling error, external disturbance, unmodeled dynamics, and parameter perturbations. The lumped disturbance and control input do not share the same coefficient matrix in the local Takagi–Sugeno (T–S) fuzzy model. In order to design a proper fuzzy disturbance observer (FDO) and involve the estimate from the FDO into controller to counteract the influence of the disturbance, system equivalence transformation is proposed in this paper. As a result, the conditions for both the asymptotical stability of the closed-loop system and the convergence of estimation error between the FDO and the disturbance are provided in the manner of linear matrix inequalities (LMIs). Also, computer simulations are provided to illustrate the effectiveness of the proposed FDO-based control system. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

The transient stability of power systems is highly affected by the changes in the power generation and load levels. Due to the variability of the generating resources, the system stability can be provoked and the system stability limits can be reached as a result of certain sudden drop in the power generation. In these cases, the load shedding can act as an effective emergency corrective action for keeping system stability; however, over-shedding of loads results in severe economical as well as social security problems. Therefore, minimization of the load shedding required for the restoration of the system stability is one of the main objectives of this paper. Another critical issue related to successful load shedding is the fast assessment of the system stability, and the amount of the load shedding as well as the implementation of the load shedding corrective action. Therefore, this paper presents a fast method of stability assessment and load shedding requirements in the weakly interconnected power system. The method is an improved form of the extended equal area criterion (EEAC) where the required system equivalence is based on the availability of wide area monitoring (WAM) devices in modern power systems. The paper also investigates the impact of the implementation duration of the required load shedding. The results are verified through time domain simulations which confirm the accuracy of the presented method and its suitability for real-time applications.

The aim of this paper is to discuss topics in contrastive morphology, combining the perspectives of morphological theory and contrastive linguistics. After an overview of the recent literature on contrastive morphology and the relevant 'tertia comparationis' in Section 2, Section 3 focuses on the main differences between compounding in Modern Greek and Italian (e.g. the position of the morphological head, the pattern stem+stem in Modern Greek vs. the pattern word+word in Italian). The diachronic dimension, the inflectional system and the role of syntax are put forward as explanatory factors for the differences between the two languages. Two recent types of compounds, [V+V] V in Modern Greek and [V+N] N in Italian, are therefore examined contrastively. The contrastive analysis of compounding is based on three types of equivalence: 'system equivalence', 'rule equivalence', and 'morphological age equivalence'. The main conclusion is that a contrastive approach to morphology enables us to deepen our understanding of both the fundamental distinction and the fundamental interconnection between morphology and syntax. © John Benjamins Publishing Company.

International audience; The periodically supported Timoshenko beam subjected to moving forces has been investigated by numerous researches. The existed models have been developed for linear supports, and this article presents a new one for nonlinear supports. By using a periodic condition and the Fourier series development, the dynamic equation of the Timoshenko beam leads to a relation between the beam displacements and the reaction forces of the supports. This relation does not depend on the support behaviour and it exists also for the Euler-Bernoulli beam. Then, the responses can be obtained by combining this relation and the constitutive law of the supports. A numerical method based on discretization of the time and frequency responses has been developed for nonlinear supports. Moreover, the influence of the beam model has been studied with numerical examples of linear and nonlinear supports. The results show that the Timoshenko beam should be used for the moving forces with high speed and/or the supports with large stiffness.

Made available in DSpace on 2019-09-12T16:26:11Z (GMT). No. of bitstreams: 0 Previous issue date: 2018 Resumo Embora a agricultura orgânica no Brasil atinja principalmente aos consumidores locais, há uma crescente demanda por pesquisas relacionadas à comercialização com o exterior neste setor. Uma pesquisa foi realizada na Europa sobre a percepção de entidades relacionadas a este tema, especificamente sobre Sistemas Participativos de Garantia (SPG), a viabilidade da equivalência entre os países e os procedimentos de controle. Um estudo exploratório foi realizado através de entrevistas com cinco organismos de certificação orgânica, dois na Suíça, três na Itália e uma associação de produtores na Itália. O SPG é pouco conhecido na Europa em geral e é sugerido divulgar melhor nos países membros. O SPG foi avaliado positivamente para reduzir os custos de certificação e promover os benefícios de um aspecto social, mas pode falhar na conformidade orgânica e na produção em grande escala. Existem diferenças significativas para estabelecer equivalência, como a falta de homogeneidade entre os países europeus em procedimentos de controle, a existência de SPG na legislação brasileira, a falta de produtos do extrativismo vegetal na Europa, diferentes períodos de conversão e a exigência de um maior número de inspeções no Brasil. A equivalência foi considerada benéfica para ambos e seria apropriado fazer esforços para torná-la viável. A legislação brasileira sobre agricultura orgânica é considerada muito restritiva e complexa. Abstract Although organic agriculture in Brazil targets mainly local consumers, there is growing demand for research related to commercializing this sector abroad. A study was done in Europe on the perception of entities related to this theme, specifically on Participatory Guarantee Systems (PGS), the feasibility of equivalence between the countries, and control procedures. An exploratory study was conducted through interviews with five organic certification bodies, two in Switzerland, three in Italy, and with a producer association in Italy. PGS is little known in Europe in general and it is suggested that it be better disseminated in the member countries. PGS has been evaluated positively for reducing certification costs and promoting benefits from a social aspect, but it can fail in organic compliance and in large scale production. There are significant differences that must be overcome in order to establish equivalence, such as the lack of homogeneity among European countries on control procedures, the existence of PGS in Brazilian legislation, lack of wild crop products in Europe, different conversion periods, and the requirement of a higher number of inspections in Brazil. Equivalence is seen as beneficial to both Europe and Brazil, and it would therefore be appropriate to promote its viability. The Brazilian law on organic agriculture is taken as very restrictive and complex. [Fortes Neto, Paulo] Universidade de Taubaté, Brazil Canavari, Maurizio] Alma mater studiorum, Italy Cavallet, Luiz Ermindo] Universidade Estadual do Paraná, Brasil

The relationship between the unimodular matrices relating coprime and column reduced matrix fraction descriptions (MFD) of a nonproper transfer function, and the restricted system equivalence (r.s.e.) transformations relating the corresponding generalised state space realisations is considered. It is shown that the r.s.e and unimodular transformations can be directly obtained from each other by inspection. The r.s.e. transformations leading to the canonical form are derived from the unimodular transformations leading to the echelon canonical form of the composite matrix of the MFD of the system.

Equivalence checking plays a crucial role in formal verification to ensure the correctness of concurrent systems. However, this method cannot be scaled as easily with the increasing complexity of systems due to the state explosion problem. This article presents an efficient procedure, based on heuristic search, for checking Milner's strong and weak equivalence; to achieve higher efficiency, we actually search for a difference between two processes to be discovered as soon as possible, thus the heuristics aims to find a counterexample, even if not the minimum one, to prove nonequivalence. The presented algorithm builds the system state graph on-the-fly, during the checking, and the heuristics promotes the construction of the more promising subgraph. The heuristic function is syntax based, but the approach can be applied to different specification languages such as CCS, LOTOS, and CSP, provided that the language semantics is based on the concept of transition. The algorithm to explore the search space of the problem is based on a greedy technique; GreASE (Greedy Algorithm for System Equivalence), the tool supporting the approach, is used to evaluate the achieved reduction of both state-space size and time with respect to other verification environments.

Summary Power system dynamic equivalence, which has been developed to overcome the computational issues, is faced with new challenges by emerging distributed energy resources (DERs). The switching characteristic between DERs operational modes beside non-dispatchable inherent, that is, generation uncertainties, should be take into account in power system dynamic equivalencing. This paper proposes a switching-based dynamic equivalence modeling for power system considering DERs. Prony analysis is employed to fit a reduced-order model to a high-order system in frequency domain. The developed modelling strategy consists of high and low frequency equivalences. When the external system reconnects to the main network through the breaker, high-frequency equivalence is replaced with external system. This period contains 4 cycles for communication delay beside 5 cycles governor time constant, which give rises to a six-order equivalence model. Afterwards, a four-order low-frequency equivalence model is fitted to the external system in the connected grid mode. Accuracy of the fitted dynamic equivalences is investigated by calculating the mean square error between the measured signal and the Prony approximated one. A synchronous-based DER, a doubly-fed induction generators and a fuel cell DER are added to the CIGRE benchmark in order to analyse the proposed dynamic equivalence modelling. Simulation results demonstrate that the proposed equivalence modelling could exhibit the same results as the real external system in the frequency domain. Simulation results also reveal that increasing penetration of DERs affect the dynamic equivalence in grid-connected mode by degrading the higher frequencies while it has no impact on transient period equivalence. Copyright © 2014 John Wiley & Sons, Ltd.

Most phrasemes contain varied semantic, stylistic, functionally pragmatic, and text-forming properties. Furthermore, phrasemes also contain additional semantic and pragmatic properties. Hence, they are regarded as complex for the translation process. Their complexity becomes even more evident during literary translation. The relationship between dictionary equivalence and text equivalence within interlingual connections is considered as particularly important. Consequently, it is observed in the present paper. The research is based on recorded instances of translated phrasemes between German as the source language and Slovene as the target language. The paper outlines how original German phrasemes were translated into Slovene, which translation procedures and strategies were applied, and to what extent dictionaries were used during the translation process. It has become evident that contrastive-linguistically defined and lexicographically documented phraseological system equivalence does not sufficiently cater for the active translator. The active translator namely principally seeks functionally pragmatic interlingual equivalence, which has to be determined in compliance with a given context. The analysis has shown many phrasemes to feature specific semantic characteristics. Consequently, the meaning of each phraseme is essentially dependent on context. Meanings of phrasemes vary significantly and can lexicographically be accurately deduced only by taking different contexts into consideration. Requirements for highlighting phraseology in dictionaries appropriately - in order for dictionaries to be applicable as viable translation aids - should therefore be based on the essential semantic characteristics of phrasemes in order to enable the user (translator) to access a vast repository of tentative translation equivalents.

Consensus problems are studied for both continuous-time and discrete-time multi-agent singular systems with time-invariant and directed communication topologies. Under restricted system equivalence of singular agents, sufficient and necessary conditions are obtained for admissible consensus ability with static protocols, which are based on both the relative information of the dynamic states and the absolute information of the static states. For a network of continuous-time singular systems, the existence of admissible consensualization can be cast into strong stabilizability of the agent dynamics. Once discrete-time multi-agent singular systems satisfy the condition of reaching nontrivial final consensus states, strong stabilizability is a sufficient condition to achieve admissible consensualization. Two algorithms are proposed to construct two protocols, which are based on a linear matrix inequality and a modified Riccati equation, respectively. Finally, the algorithms are illustrated by two simulation examples.

Checking if a given system implementation respects its specification is often done by proving that the two are ''equivalent''. The equivalence is chosen, in particular, for its computability and of course for its meaning, that is, for its adequacy with what is observable from the two systems (implementation and specification). Trace equivalence is easily testable (decidable from interaction), but often considered too weak; in contrast, bisimulation is accepted as the canonical equivalence for interaction, but it is not testable. Richer than an equivalence is a form of distance: it is zero between equivalent systems, and it provides an estimation of their difference if the systems are not equivalent. Our main contribution is to define such a distance in a context where (1) the two systems to be compared have a stochastic behavior; (2) the model of one of them (e.g., the implementation) is unknown, hence our only knowledge is obtained by interacting with it; (3) consequently the target equivalence (observed when distance is zero) must be testable. To overcome the problem that the model is unknown, we use a Reinforcement Learning approach that provides powerful stochastic algorithms that only need to interact with the model. Our second main contribution is a new family of testable equivalences, called K-moment. The weakest of them, 1-moment equivalence, is trace equivalence; as K grows, K-moment equivalences become finer, all remaining, as well as their limit, weaker than bisimulation. We propose a framework to define (and test) a bigger class of testable equivalences: Test-Observation-Equivalences (TOEs), and we show how they can be made coarser or not, by tuning some parameters.

In this paper, a new approach for stability analysis of time-dependent switched linear systems is proposed. System equivalence is the main idea in this new approach, which derives a switched discrete linear parameter-varying system from the switched continuous-time linear switched system with interval dwell time, and the stability properties of the two corresponding systems are proved to be equivalent. Then, by applying a quadratic Lyapunov function approach for the equivalent switched discrete system, the stability of the switched continuous-time linear system can be established without checking any average dwell time condition. Finally the computation complexity is analyzed, and mode incidence matrix is introduced to reduce the computation cost.

International audience; In this study, a novel model for a periodically supported beam subjected to moving loads was developed using a periodicity condition on reaction forces. This condition, together with Fourier transforms and Dirac combs properties, forms a relation between the beam displacement and support reaction forces. This relation explains the force distribution to the supports, and holds for any type of support and foundation behaviors. Based on this relation, a system equivalence for a periodically supported beam is presented in this paper. An application to nonballasted viscoelastic supports is presented as an example and the results clearly match the existing model. Next, an approximation of real-time responses was developed for the moving loads as periodical series. The comparison shows that this approximation can be used for a limited number of loads if the distances between loads are sufficiently large. The system equivalence for a periodically supported beam is efficient for supports with linear behavior, and could be developed for other behaviors.

An efficient systematic procedure is provided for symbolic computation of Lie groups of equivalence transformations and generalized equivalence transformations of systems of differential equations that contain arbitrary elements (arbitrary functions and/or arbitrary constant parameters), using the software package GeM for Maple. Application of equivalence transformations to the reduction of the number of arbitrary elements in a given system of equations is discussed, and several examples are considered. First computational example of a generalized equivalence transformation where the transformation of the dependent variable involves the arbitrary constitutive function is presented. As a detailed physical example, a three-parameter family of nonlinear wave equations describing finite anti-plane shear displacements of an incompressible hyperelasic fiber-reinforced medium is considered. Equivalence transformations are computed and employed to radically simplify the model for an arbitrary fiber direction, invertibly reducing the model to a simple form that corresponds to a special fiber direction, and involves no arbitrary elements. The presented computation algorithm is applicable to wide classes of systems of differential equations containing arbitrary elements., Comment: In review for publication

A recent paper by Karin et al. introduced a mathematical notion called dynamical compensation (DC) of biological circuits. DC was shown to play an important role in glucose homeostasis as well as other key physiological regulatory mechanisms. Karin et al. went on to provide a sufficient condition to test whether a given system has the DC property. Here, we show how DC can be formulated in terms of a well-known concept in systems biology, statistics, and control theory—that of parameter structural non-identifiability. Viewing DC as a parameter identification problem enables one to take advantage of powerful theoretical and computational tools to test a system for DC. We obtain as a special case the sufficient criterion discussed by Karin et al. We also draw connections to system equivalence and to the fold-change detection property., Author summary A recently introduced mathematical notion called dynamical compensation of biological circuits was shown to play an important role in glucose homeostasis and other key physiological regulatory mechanisms. This paper explains how dynamical compensation can be formulated in terms of a well-known concept in systems biology, statistics, and control theory—that of parameter structural non-identifiability. Viewing dynamical compensation as a parameter identification problem enables one to take advantage of powerful theoretical and computational tools to test a system for dynamical compensation. As a special case, one obtains the sufficient criterion for dynamical compensation. The paper also draws connections to system equivalence and to the fold-change detection property. The non-identifiability characterization brings up an interesting contrast in the way in which one thinks of these properties in the two fields. From the point of view of robustness of behavior, one wishes that parameters do not influence much the response of a system. On the other hand, from the systems and parameter identification point of view, the more that a parameter affects behavior, the easier it is to estimate it, and poor sensitivity is taken as an indication of a poorly parametrized model.

In this paper we consider continuous-time stochastic linear control systems and study the notion of stochastic external behaviour equivalence. Starting from our earlier work on equivalences given for discrete-time stochastic control systems, we first extend the notion of stochastic external behaviour equivalence and the corresponding geometric conditions to the continuous-time framework. We then address model reduction and we show that the system with minimal dimension in the state space which has equivalent stochastic external behavior of a system, can be easily obtained by factoring out the unobservable dynamics from the given system. Connections with equivalence notions given for nondeterministic linear control systems and with stochastic linear realization theory are also formally discussed.

In this paper, we exploit motion for improving the ultrasound (US) imaging performance of thinned sensor array systems. Thinned arrays provide reduced system cost and allows for the reduction of bulky channel cables. However, thinned array systems suffer from poor array processing performance from the lack of channels available to the system when compared to a Uniform Linear Array (ULA). To overcome these deficiencies we propose to use motion to augment the transmit/receive events such that a general thinned array can be made to perform statistically equivalently to a ULA. The key feature of this work is that the statistical equivalence does not depend on realizing all missing sensors, instead the equivalence is at the level of the sum co-array. We show simulation results that demonstrate the system equivalence of thinned arrays with about one-third of the active sensors compared to a ULA of equal aperture.

Electromagnetic transient simulation for large-scale power system is a time-consuming problem. A new frequency-dependent equivalence method is presented in the paper, which might significantly accelerate power system electromagnetic transient simulation. In the method, an effective algorithm is designed to directly transfer the port admittance determinant of external system’s mixing matrix into admittance rational function; and the step-by-step strategy for the equivalence of actual large system is put forward, which further reduces the calculation quantities needed. Moreover, the study of multiple real root pole characteristics of admittance transfer function of two-port network is performed and a proposition is achieved. Based on the proposition and residue theorem, the equivalence system for external system corresponding to the admittance rational function is obtained. The computation complexity of the step-by-step equivalence method is about o(⌋n/np⌉×t)(⌋⌉ is upper integral operation, n is the total buses number of external system, NP is the total buses number of single step equivalence network, T is single step equivalence time), which indicates that the computation complexity of the method proposed has nearly linear relationship with the buses number of external system, and the method proposed has satisfactory computation speed. Since the mixing matrix of external system includes all the information of external system, therefore, port admittance rational function derived from it can reflect its full frequency characteristic and the equivalence network achieved has high equivalence precision. Moreover, since the port rational function is gained at the condition of the external system without source, which equals stable passive network, it could not show any unstable pole and need not extra measure to make the equivalence system stable. The test results of the samples and comparison with other methods demonstrate that the new method proposed is valid and effective.

The connection between the polynomial matrix descriptions (PMDs) of the well-known regular and singular 2D linear discrete state space models is considered. It is shown that the transformation of strict system equivalence in the sense of Fuhrmann provides the basis for this connection. The exact form of the transformation is established for both the regular and singular cases.

When the scale of wind farm is increased quickly, if not considering the impedance of the collection system within wind farm, the bigger error in power flow calculation may be caused. In this paper a simple equivalence method calculating the collector system equivalence impedance by using the equivalence power loss is proposed and wind farm’s equivalence output power model considering wake effect and wind speed is established. The models are applied in power flow calculation of the natural wind farm connected to Urumqi grid, Xinjiang. The results compared with original system power flow show that this method has lower error. By using the losses in the collector system, the method of computing the equivalence impedance is verified in this paper. The equivalence impedance of collector system is calculated from total active power loss and total reactive power loss and current flow of the collector system. The error analysis showed that the equivalence impedance of collector system has lower error. The test results show that the proposed equivalence method is effective and logical and has a certain practicality. The reference is given for farther studying safety and stability operation of electric power system including wind farm.

In this article. First, we construct some nonlinear differential systems which are equivalent to some known systems. Second, we discuss, in a different method, the equivalence between some linear differential systems. And then we apply the obtained results to the study of the qualitative properties of these systems simultaneously.

This paper considers linear dynamical systems restricted to square integrable trajectories. Following the behavioral formalism, a number of relevant classes of linear and shift-invariant L"2 systems are defined. It is shown that rational functions, analytic in specific half-spaces of the complex plane, prove most useful for representing such systems. For various classes of L"2 systems, this paper provides a complete characterization of system equivalence in terms of rational kernel representations of L"2 systems. In addition, a complete solution is given for the problem when selected (non-manifest) variables of an L"2 system can be completely eliminated from their behavior. This elimination theorem has considerable independent interest in general modeling problems. It is shown that the elimination result is key in the solution of the problem for realizing an arbitrary L"2 system as the interconnection of a given L"2 system and a to-be-synthesized L"2 system. In the context of control, this problem amounts to characterizing the existence and parameterization of all controllers that, after interconnection with a given plant, constitute a desired controlled system.

Linear parameter-varying (LPV) systems are usually described in either state-space or input-output form. When analyzing system equivalence between different representations it appears that the time-shifted versions of the scheduling signal (dynamic dependence) need to be taken into account. Therefore, representations used previously to define and specify LPV systems are not equal in terms of dynamics. In order to construct a parametrization-free description of LPV systems that overcomes these difficulties, a behavioral approach is introduced that serves as a basis for specifying system theoretic properties. LPV systems are defined as the collection of trajectories of system variables (like inputs and outputs) and scheduling variables. LPV kernel, input-output, and state-space system representations are introduced with appropriate equivalence transformations.

In this note the question of system equivalence for linear dynamical systems is studied in full generality (and in the algebraic style).

A new efficient method for finding generalized equivalence transformations for a class of differential equation systems via its related extended classical symmetries is presented. This technique can be further adapted to find the equivalence transformations for the mathematical model. It applies to classes of differential systems whose arbitrary functions involve all equations’ independent variables. As a consequence, any symbolic manipulation program designed to find classical Lie symmetries can also be used to determine generalized equivalence transformations and equivalence transformations, respectively, without any modification of the program. The method has been implemented as the maple routine gendefget and is based on the maple package desolv(by Carminati and Vu). The nonlinear stationary heat conduction parameter identification problem is considered as an example.

In this paper we explore equivalence conditions and invariants for behaviors given in kernel representations. In case the kernel representation is given in terms of a linear matrix pencil, the invariants for strict equivalence are given by the Kronecker canonical form which, in turn, we interpret in geometric control terms. If the behavior is given in a kernel representation by a higher order rectangular polynomial matrix, the natural equivalence concept is behavior equivalence. These notions are closely related to the Morse group that incorporates state space similarity transformations, state feedback, and output injection. A simple canonical form for behavioral equivalence is given that clearly exhibits the reachable and autonomous parts of the behavior. Using polynomial models we also present a unified approach to pencil equivalence that elucidates the close connections between classification problems from linear algebra, geometric control theory, and behavior theory. We also indicate how to derive the invariants under behavior equivalence from the Kronecker invariants.

Nonlinear control systems on homogeneous time scales are studied. First the concepts of reduction and irreducibility are extended to higher order delta-differential input-output equations. Subsequently, a definition of system equivalence is introduced which generalizes the notion of transfer equivalence in the linear case. Finally, the necessary and sufficient conditions are given for the existence of a state-space realization of a nonlinear input-output delta-differential equation.

We show that stabilizing tracking proportional-integral (PI) controllers can be constructed for minimum-phase nonaffine-in-control systems. The constructed PI controller is an equivalent realization of an approximate dynamic inversion controller. This equivalence holds only for the time response when applied to the unperturbed system. Even when restricted to unperturbed minimum-phase linear time invariant systems, their closed loop robustness properties differ. This shows that in general, properties that do not define the equivalence relation for systems/controllers are not preserved under such equivalence transformations.