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In this paper, we address the group controllability issue for discrete-time multi-agent systems (MASs) with two-time-scale feature. Since the existence of singular perturbation parameter in modeling the two-time-scale MASs will cause ill-posedness problems, we decouple the MASs into fast and slow subsystems by using the iterative and approximate methods, and then eliminate the singular perturbation parameter. By using matrix theory, we propose a lot of necessary and/or sufficient conditions of group controllability, where some easy-to-use criteria are determined only by eigenvalues of matrices. Lastly, a simulation example is given to illustrate the effectiveness of the proposed theoretical results.

In this study, the controllability of multi-agent systems with second-order dynamic under discrete-time model, which evolve on two time scales. The authors first characterise the systems by difference equations with a singular perturbation parameter. Then, in order to get rid of the singular perturbation parameter, they split the systems into a slow subsystem and fast subsystem based on the iterative method and approximate approach. Moreover, according to matrix theory, they deduce a lot of necessary and/or sufficient controllability criteria of the systems. In particular, a second-order controllability criterion only depending on the eigenvalues of matrices is proposed, which is more easy-to-use and efficient. A simulation example is lastly given to clarify the validity of all theoretical results.

This work is concerned with competitive Lotka–Volterra model with Markov switching. A novelty of the contribution is that the Markov chain has a countable state space. Our main objective of the pap...

This paper addresses the controllability for an interconnected two-time-scale second-order multi-agent system. Firstly, to eliminate the singular perturbation parameter, we separate the multi-agent system into slow subsystem and fast subsystem by using singular perturbation methods. Then, based on matrix theory, some necessary and/or sufficient criteria are derived for second-order controllability of two-time-scale multi-agent systems with multiple leaders. Moreover, we propose some easy-to-use second-order controllability criteria determined only by eigenvalues of system matrices. Lastly, the effectiveness of the proposed theoretical results is illustrated by a simulation example.

This paper investigates the controllability of discrete-time leader-follower multiagent systems (MASs) with two-time-scale and heterogeneous features, motivated by the fact that many real systems are operating in discrete-time. In this study, singularly perturbed difference systems are used to model the two-time-scale heterogeneous discrete-time MASs. To avoid the ill-posedness problem caused by the singular perturbation parameter when using the classical control theory to study the model, the singular perturbation method was first applied to decompose the system into two subsystems with slow-time-scale and fast-time-scale feature. Then, from the perspective of algebra and graph theory, several easier-to-use controllability criteria for the related MASs are proposed. Finally, the effectiveness of the main results is verified by simulation.

As a basic concept in modern control theory, controllability reveals the fundamental structural characteristics of a dynamic system, and it also plays an important part in the analysis and control of a dynamic system. With the increasing complexity of multi-agent systems, the multi-agent networks can be divided into some subnetworks in terms of time scales. This paper concentrates on the group controllability of two-time-scale multi-agent networks, establishes the necessary and sufficient criterion of group controllability based on singular perturbation methods, and deduces easy-to-use group controllability criteria by using matrix theory and graph theory. Lastly, a simulation example is presented to illustrate the effectiveness of the proposed methods.

In transient stability analysis, the fifth-order generator model neglects the stator transients and may result in different simulation results as compared with the seventh-order model. Based on the two-time scale property of generators, a dynamic correction method is proposed to offset the difference. Using the singular perturbation theory, fast components in the stator flux linkage is captured to restore stator dynamics and correct the electromagnetic torque. Simulations on a single-machine-infinite-bus (SMIB) system and a 3-machine system show that, the difference between the two generator models can be remarkably reduced by the proposed method.

This paper reviews some results from the theory of two-time scale dynamical systems (also called fast-slow systems) and presents the detailed analysis of some systems of interest in electrical engineering and fusion plasma physics. The aim of this work is to introduce engineers to singular perturbation methods as a tool for providing additional insights in modeling and understanding systems whose components evolve on different time scales.

In this paper, we investigate the controllability problems for heterogeneous multiagent systems (MASs) with two-time-scale feature under fixed topology. Firstly, the heterogeneous two-time-scale MASs are modeled by singular perturbation system with a singular perturbation parameter, which distinguishes fast and slow subsystems evolving on two different time scales. Due to the ill-posedness problems caused by the singular perturbation parameter, we analyze the two-time-scale MASs via the singular perturbation method, instead of the general methods. Then, we split the heterogeneous two-time-scale MASs into slow and fast subsystems to eliminate the singular perturbation parameter. Subsequently, according to the matrix theory and the graph theory, we propose some necessary/sufficient criteria for the controllability of the heterogeneous two-time-scale MASs. Lastly, we give some simulation and numerical examples to demonstrate the effectiveness of the proposed theoretical results.

This paper proposes a two-time scale simulation approach of both short-term and long-term dynamics in power systems. The short-term transient period is analyzed by a full-time scale simulation while a quasi-steady state model of the power system is used to simulate long-term dynamics. The proposed method is inspired of Singular Perturbation theory to model the interaction between the short-term and long-term dynamics. Based on this interaction, a suitable criterion to determine when the quasi-steady state model of a power system can be considered as a uniform approximation of the full-time scale model is proposed, which also determines the appropriate switching time between models. The proposed method is demonstrated on the 10-machine, 39-bus New England system and a 46-machine, 190-bus equivalent Mexican system.

The present paper has two main purposes. The first is to provide an explicit state-space solution of the robust stabilization problem with respect to the NLCF for two-time scale systems. In this construction only the solutions of the control and of the filtering Riccati equations associated with the slow and with the fast dynamics of the nominal plant are used. These solutions do not depend upon the singular perturbation and therefore all computations are well-conditioned. The second purpose of the paper is to investigate the case when an k -independent robust controller can be used for the robust stabilization of a two-time scale nominal system. Two constructions of such controllers are developed under some additional assumptions. Numerical examples illustrate the theoretical developments.

In this paper, we address the dynamic modeling of reactive distillation processes, where the presence of fast reaction or momentum transport induces two time scale dynamics. We present a systematic modeling framework that allows identifying the source of time Scale multiplicity and deriving nonlinear non-stiff models of the slow dynamics.

This note considers the problem of robustness of discrete two-time-scale systems. Robustness is first analyzed for a nominal system as the general e-bound problem which characterizes an upper bound of the singular perturbation parameter. The stability robustness is then extended to handle the problem of systems subject to parameter variations. For any singular perturbation parameter bounded above by that obtained from the e-bound problem, a stability robustness bound with respect to parameter variations is derived. The results include both unstructured and structured variations.

This paper focuses on the synthesis of well-conditioned multivariable robust controllers for a broad class of multi-input multi-output two-time-scale nonlinear systems with time-varying uncertain variables, modeled within the framework of singular perturbations. The proposed controller stabilizes the fast dynamics, guarantees boundedness of trajectories, and ensures that the ultimate discrepancy between the outputs and the external reference inputs in the closed-loop system can be made arbitrarily small by an appropriate choice of controller parameters, provided that the singular perturbation parameter is sufficiently small. The developed control method is tested, through simulations, on a fluidized catalytic cracking reactor.

This paper describes a fundamental study into modeling the effects of frequency variation on network and shunt impedances in long term power system stability simulations. The focus is on extreme post-fault situations where significant generation-load mismatch causes wide excursions in power system frequency. A novel application of singular perturbations is presented. This method is compared with the "constant reactance" technique, the "variable reactance" method in which the network reactances are varied with system frequency, and a method in which the network transients are fully simulated. Stability simulations for an interconnected two-area power system employing the different modeling techniques show that a two time scale analysis using the singular perturbation method is a feasible technique for accurate prediction of long term post fault system behaviour.

In the quarter car model, the active suspension with nonlinear characteristics is investigated. An active suspension model is made by two time scale modeling. Two models have relation to handling and the ride comfort respectively. A new control method that is based on the singular perturbation approach is proposed. Our control law for the full model combines with control laws for slow and fast submodels. The simulation shows that the new design approach is very useful.

Multi-rate control design of two-time-scale systems is considered via digital redesign method. After the multi-rate control design procedures via singular perturbation theory is reviewed and the relationships between slow and fast subproblems are clarified, the design method via the bi-linear transformation method is investigated. Furthermore, in order to verify the validity of this method, an application to the longitudinal control problem of an aircraft is given.

A decentralized model predictive controller applicable for some systems which exhibit different dynamic characteristics in different channels was presented in this paper. These systems can be regarded as combinations of a fast model and a slow model, the response speeds of which are in two-time scale. Because most practical models used for control are obtained in the form of transfer function matrix by plant tests, a singular perturbation method was firstly used to separate the original transfer function matrix into two models in two-time scale. Then a decentralized model predictive controller was designed based on the two models derived from the original system. And the stability of the control method was proved. Simulations showed that the method was effective.

In this paper we propose a robust redesign technique which recovers the trajectories of a nominal control design in the presence of additive input uncertainties. We design a high-gain filter and employ the fast variables arising from this filter in the feedback control law to cancel the effect of the uncertainties in the plant. Using singular perturbation theory we prove that the trajectories of the redesigned system approach those of the nominal system when the filter gain is increased. We illustrate the redesign by applying it to two physically motivated examples.

Active pneumatic vibration isolators have been widely studied as the use of precision equipment increases. This paper focuses on the robust two-time-scale control design of an active pneumatic vibration isolator using the singular perturbation method and time delay control (TDC). The singular perturbation method, or more generally, the two-time-scale approach to feedback design is used to cope with the ill-conditioning of the pneumatic vibration isolator; TDC is used to overcome inevitable modeling errors in more accurate physical model of pneumatic vibration isolator and unknown disturbance such as base excitation. Because the proposed controller in this paper is based on more accurate physical model than rough model, accurate control is feasible. Numerical experiment demonstrates the effectiveness of the proposed robust two-time-scale control design.

The singular perturbation approach to the analysis and design of two-time-scale systems is applied to the H/sub /spl infin// filtering problem. A sequential procedure is described to decompose the problem into slow and fast subproblems. In this procedure, a fast filter is designed first using the fast model; then a slow filter is designed under a condition on the value of the filter at infinity. A composite filter is formed as the parallel connection of the fast with the strictly proper part of the slow filter. The asymptotic validity of the composite filter is established.

This paper focuses on multivariable two-time-scale nonlinear control systems with disturbances, modeled within the mathematical framework of singular perturbations. For such systems, we synthesize well-conditioned control laws that stabilize the fast dynamics, enforce a prespecified input/output response, eliminate the effect of disturbances on the output and guarantee boundedness of trajectories of the closed-loop system, for sufficiently small values of the singular perturbation parameter.

The objective of this paper is to design a compensator by a singular perturbation approach for flexible structures subjected to moving vibratory system (e.g. bridge vibration system with moving vehicle). The proposed design of the controller includes a composite control strategy derived by the singular perturbation approach. In order to overcome the problem of lack of full state availability, a compensator is applied to the controller. Using this compensator, the vibration amplitude of the elastic beams can be reduced and the performance of the dynamic system improved. Although the research idea originated from exploration of the dynamic characteristics of the bridge system, the findings of this paper can be applied to various mechanical systems such as space structures, ballistic systems, gantry crane, and other dynamic systems with moving loads.

Output feedback control of linear time-invariant singularly perturbed systems is studied. The set of all compensators that stabilize a singularly perturbed system while preserving its two-time-scale structure is parameterized. The parameterization is used to show that any two-frequency-scale stabilizing compensator can be asymptotically approximated by a compensator designed via a sequential procedure. In this procedure, a fast (high-frequency) compensator is designed first to stabilize the fast model of the system. Then, a strictly proper slow (low-frequency) compensator is designed to stabilize a modified slow model. The parallel connection of the two compensators forms a two-frequency-scale stabilizing compensator for the singularly perturbed system.

The block processing technique is applied to a class of two-time-scale linear discrete-time systems. Block state-space structures for slow and fast subsystems have been obtained. Based upon these models, blocked slow and fast controls are designed. In addition, an extra control is designed to exactly compensate for the effects of the parasitics.

The design of stabilizing feedback control of singularly perturbed diserete-time systems is decomposed into the design of slow and fast controllers which are combined to form the composite control. Composite control strategies are developed for the case of single rate measurements (all variables are measured at the same rate) as well as for the case of multirate measurements (slow variables are measured at a rate slower than that of fast variables).

The stabilization of a class of singularly perturbed linear time-varying systems is considered through the separate stabilization of two lower dimensional subsystems in two different time-scales. A composite stabilizing controller is synthesized from the separate stabilizing controllers of the two subsystems, the mutually independent gains of which do not require knowledge of the small singular perturbation parameter.

The design of a state feedback controller for a two-time-scale discrete-time system is considered via a two-stage design approach. After discrete-time modelling via slow and fast sampling rates has been discussed, state feedback design approaches for the fast sampling model (i.e. the two-stage design approach and the direct approach) are studied, and the relation between them is clarified. Following these results, the eigenvalue assignment and the stabilizing problems are investigated.

This paper contains a brief discussion of various model simplification techniques currently available in the literature. The main intention is to highlight some of the unifying features of the different model simplification techniques. Directions for possible future research are also indicated.