Stability Of Large-scale Systems Research Articles

Consensus of multi-agent systems and stabilization of large-scale systems with time delays and nonlinearities - a comparison of both problems

Consensus of multi-agent systems and stabilization of large-scale systems with time delays and nonlinearities - a comparison of both problems

Dynamic modeling and small signal stability analysis of distributed photovoltaic grid-connected system with large scale of panel level DC optimizers

The distributed maximum power point tracking (DMPPT) technologies, based on a DC optimizer (DCO) for every single photovoltaic (PV) panel, are increasingly proposed to mitigate the waste of solar energy due to the mismatch problems of PV arrays. However, the stability problem of DMPPT based distributed PV grid-connected systems that involve a large amount of DCOs remains to be further studied. Therefore, modeling, deservedly, is the basis for stability analysis. Usually the model of the PV power plant consists of hundreds or even thousands of DCOs, which results in a heavy computation burden during the simulation. To solve the modeling problem, this paper proposes a matrix variables based modeling method for the distributed PV grid-connected system. The core idea of the modeling method is to convert the complex model that contains plenty of PV-DCO generation units to an average model consisting of only two typical submodules, by constructing the block matrix formed variables. In this way, the model has the advantages of good scalability and high simulation efficiency, and can be realized by the vector simulation feature of Matlab/Simulink. Besides, it is easy to obtain the linearization results directly by using the Linearization Toolbox in Simulink, which avoids the complexity of writing programs for linearization calculation when studying the stability of large-scale systems. Based on the average model and corresponding linearization results, the key impacts on the small signal stability of the system are determined via the eigenvalue analysis method and root locus method. It is shown that the total active power output by PV array, the controller parameters of the grid-connected inverter, and the strength of the AC system are critical factors affecting the small signal stability of distributed PV grid-connected system. Different simulation results verify the effectiveness of the proposed approach.

Simultaneous Stability of Large-scale Systems via Distributed Control Network with Partial Information Exchange

This paper is concerned with the simultaneous stability of the multi-mode large-scale systems composed of the interaction subsystems. A novel distributed control network consisting of multiple network-based controllers with the partial information exchange is adopted to simultaneously stabilize the large-scale systems in multiple operation modes. In the distributed control network (DCN), a partial state information exchange approach is developed to save the real-time communication and computation resources. To compensate for the effects of dynamic couplings between interaction subsystems, the designed controllers use both the local states and the neighbors’ partial information with packet dropouts for local feedback design. Then, a series of Lyapunov functions are constructed to derive a matrix-inequality-based sufficient condition for the existence of the desired controllers. Based on an orthogonal complement technique, the gains of the controllers in DCN are parameterized. The iterative algorithm for the solution of simultaneous stabilization problem is also developed. Finally, a numerical example is performed to show the relevant feature of the proposed method.

Simultaneous H∞ stabilization for large-scale systems within distributed wireless networked control framework over fading channels

In this paper, the simultaneous H∞ stabilization problem is investigated for a physically interconnected large-scale system which works in multiple operation modes. A distributed wireless networked control framework is introduced, in which the distributed dynamic output feedback controllers not only use the local measurements, but also receive the neighboring controllers’ broadcasts via wireless networks. The channel fading in wireless communications is described as the Rice fading model. Our focus is on the design of the distributed controllers such that the large-scale system is mean-square stable in each operation mode and achieves a prescribed H∞ disturbance attenuation level. By employing the Lyapunov functional method and related stochastic analysis techniques, a sufficient condition on the existence of desired controllers is presented, and the parameterization of the controller gains is derived. Finally, a numerical example is utilized to illustrate the feasibility of the proposed scheme.

Finite-Time Stability of Large-Scale Systems with Interval Time-Varying Delay in Interconnection

We investigate finite-time stability of a class of nonlinear large-scale systems with interval time-varying delays in interconnection. Time-delay functions are continuous but not necessarily differentiable. Based on Lyapunov stability theory and new integral bounding technique, finite-time stability of large-scale systems with interval time-varying delays in interconnection is derived. The finite-time stability criteria are delays-dependent and are given in terms of linear matrix inequalities which can be solved by various available algorithms. Numerical examples are given to illustrate effectiveness of the proposed method.

Robust Exponential Stability of Large-Scale System With Mixed Input Delays and Impulsive Effect

In this paper, a class of large-scale systems with impulsive effect, input disturbance, and both variable and unbounded delays were investigated. On the assumption that all subsystems of the large-scale system can be exponentially stabilized, and the stabilizing feedbacks and corresponding Lyapunov functions (LFs) for the closed-loop systems are available, using the idea of vector Lyapunov method and M-matrix property, the intero-differential inequalities with variable and unbounded delays were constructed. By the stability analysis of the intero-differential inequalities, the sufficient conditions to ensure the robust exponential stability of the large-scale system were obtained. Finally, the correctness and validity of the methods was verified by two numerical examples.

Distributed non-fragile stabilization of large-scale systems with random controller failure

This paper is concerned with the distributed stabilization of large-scale systems with gain variation and controller failure. The so-called distributed non-fragile control problem is firstly studied and a set of random variables are introduced to model the controller failure phenomenon. Based on the Lyapunov stability theory and some stochastic system analysis method, a sufficient condition is obtained such that the closed-loop system is asymptotically stable in the mean-square sense and achieves a prescribed H∞ performance level. A simulation study on the interconnected inverted pendulums is given to show the effectiveness of the proposed controller design method.

Decentralized measurement feedback stabilization of large-scale systems via control vector Lyapunov functions

This paper studies the problem of decentralized measurement feedback stabilization of nonlinear interconnected systems. As a natural extension of the recent development on control vector Lyapunov functions, the notion of output control vector Lyapunov function (OCVLF) is introduced for investigating decentralized measurement feedback stabilization problems. Sufficient conditions on (local) stabilizability are discussed which are based on the proposed notion of OCVLF. It is shown that a decentralized controller for a nonlinear interconnected system can be constructed using these conditions under an additional vector dissipation-like condition. To illustrate the proposed method, two examples are given.

Disturbance and Delay Robustness Guarantees of Gradient Systems Based on Static Noncooperative Games With an Application to Feedback Control for PEV Charging Load Allocation

This paper investigates robustness of gradient-type dynamical systems derived from static noncooperative games with a large number of players. The control objective is to drive state variables to the vicinities of Nash equilibria in the presence of disturbance and time-delay. The framework of integral input-to-state stability for large-scale systems is employed for verifying such global robustness. Several robustness criteria are presented, and Lyapunov-Krasovskii functionals are constructed. The developed theory is applied to the plug-in electric vehicle charging problem of allocating the charging load to the overnight demand valley to reduce the impact on the electric grid. Securing robustness of the dynamic load allocation is important, since eliminating uncertainties in demand predictions would become harder due to energy storage integration coupled with various energy-aware technologies. Introducing feedback, this paper guarantees stability and achieves robustness of the allocation dynamics subject to communication delay when demand predictions are not accurate. The usefulness of the proposed decentralized scheme is illustrated by numerical simulations.

Decentralized stabilization of large-scale systems with interval time-varying delays in interconnections

SUMMARY This paper considers decentralized stabilization problem for a class of large-scale systems with interval time-varying delays in interconnections. The time delay is assumed to be a continuous function belonging to a given interval but not necessary to be differentiable. On the basis of constructing a set of improved Lyapunov–Krasovskii functionals, new sufficient conditions for the existence of decentralized state feedback controller are established in terms of linear matrix inequalities. The decentralized control design guarantees the system exponential stability. An illustrative example is given to show the validity of the results obtained in this paper. Copyright © 2012 John Wiley & Sons, Ltd.

Connection between cooperative positive systems and integral input-to-state stability of large-scale systems

We consider a class of continuous-time cooperative systems evolving on the positive orthant R + n . We show that if the origin is globally attractive, then it is also globally stable and, furthermore, there exists an unbounded invariant manifold where trajectories strictly decay. This leads to a small-gain-type condition which is sufficient for global asymptotic stability (GAS) of the origin. We establish the following connection to large-scale interconnections of (integral) input-to-state stable (ISS) subsystems: If the cooperative system is (integral) ISS, and arises as a comparison system associated with a large-scale interconnection of (i)ISS systems, then the composite nominal system is also (i)ISS. We provide a criterion in terms of a Lyapunov function for (integral) input-to-state stability of the comparison system. Furthermore, we show that if a small-gain condition holds then the classes of systems participating in the large-scale interconnection are restricted in the sense that certain iISS systems cannot occur. Moreover, this small-gain condition is essentially the same as the one obtained previously by Dashkovskiy, Rüffer, and Wirth (2007, in press) for large-scale interconnections of ISS systems.

Conservatism Reduction in Two-level Control for Stabilization of Discrete Large Scale Systems

摘要: The aim of this paper is to propose a new algorithm for multilevel stabilization of large scale systems. In two-level stabilization method, a set of local stabilizers for the individual subsystems in a completely decentralized environment is designed. The solution of the control problem involves designing of a global controller on a higher hierarchical level that provides corrective signals to account for interconnections effect. The principle feature of this paper is to reduce conservativeness in global controller design. Here, the key point is to reduce the effect of interactions instead of neutralizing them. In fact, unlike prior methods, our idea does not ignore the possible beneficial aspects of the interactions and does not try to neutralize them. 关键词: Large scale systems / two-level control / stability / conservatism reduction

Conservatism Reduction in Two-level Control for Stabilization of Discrete Large Scale Systems

The aim of this paper is to propose a new algorithm for multilevel stabilization of large scale systems. In two-level stabilization method, a set of local stabilizers for the individual subsystems in a completely decentralized environment is designed. The solution of the control problem involves designing of a global controller on a higher hierarchical level that provides corrective signals to account for interconnections effect. The principle feature of this paper is to reduce conservativeness in global controller design. Here, the key point is to reduce the effect of interactions instead of neutralizing them. In fact, unlike prior methods, our idea does not ignore the possible beneficial aspects of the interactions and does not try to neutralize them.

On parametric asymptotic stability of large-scale systems

The domain of parameter values in which an autonomous large-scale system is uniformly asymptotically stable is estimated. The comparison method with a vector Lyapunov function is chosen for analysis

Aggregation and stability analysis of nonlinear complex systems

The problem of stability of large-scale systems in critical cases is investigated. New form of aggregation for essentially nonlinear complex systems is suggested. With the help of this form the sufficient conditions of asymptotic stability are determined. The results obtained are used for the stability analysis of complex systems by the nonlinear approximation and for the investigation of absolute stability conditions for a certain class of nonlinear systems.

Failure-tolerant performance stabilization of the generic large-scale system by decentralized linear output feedback

Most of the existing results on the decentralized stabilization of large-scale systems consider systems in the input-output-decentralized form, i.e., systems whose input and output matrices are block diagonal. The controller synthesis for such systems is less involved than that for input-output-centralized ones. In this paper, a transformation is proposed for the input-output decentralization of the generic large-scale system. Using the transformed system, a sufficient condition for failure-tolerant performance stabilization of the original large-scale system in a desirable performance region under decentralized linear output feedback is established. The problem is then reformulated as a constrained nonlinear optimization problem. The proposed methodology results in the optimal reconciliation of failure-tolerant performance stabilization of the overall system, and reliability and low actuator gains of the isolated subsystems. The effectiveness of the proposed approach is demonstrated by an example.

Connective Stability of Large Scale Systems: Revisited

In this paper, connective stability is considered for large scale systems consisting of a number of subsystems and uncertain interconnections. A necessary and sufficient condition of connective stability is derived in terms of linear matrix inequalities (LMIs), under which the overall systems are robustly stable against the uncertainties of the interconnections. This condition gives a useful sufficient condition which lead to an LMI condition even for connective stabilization via decentralized state feedback if an unstructured matrix variable in the LMIs is restricted to a block diagonal one. In this paper, a characterization of this sufficient condition is also derived in frequency domain. It is shown that the condition is equivalent to a familiar ℳ matrix condition which utilizes ℋ∞ norm of each subsystem.

The Behavioral Approach to Simultaneous Stabilization for Large Scale Systems

In this paper, we address simultaneous stabilization problem for two linear plants in a behavioral framework. Particularly, we provide a necessary and sufficient condition for two linear plants to be simulatneously stabilizable and extract a symmetric structure of simultaneous stabilizers with respect to the behavioral interconnection which corresponds to synthesis of not only feedback controllers but also system structures.

Numerical stability analysis of a large-scale delay system modeling a lateral semiconductor laser subject to optical feedback.

This paper highlights the use of advanced numerical tools to study the stability of large-scale systems of delay differential equations (DDEs). Specifically, we consider a model describing a semiconductor laser subject to conventional optical feedback and lateral carrier diffusion. The symmetry of the governing rate equations allows external cavity mode solutions (ECMs) to be computed as steady state solutions. Using the software package DDE-BIFTOOL, branches of ECMs are computed as a function of varying feedback strength. The stability along these branches is computed by solving eigenvalue problems, the size of which is governed by a step-length heuristic. In this paper, we employ an improved heuristic which substantially reduces the size of these eigenvalue problems. This approach makes the stability analysis of large-scale systems of DDEs computationally feasible.

Decentralized stabilization of large-scale systems via state-feedback and using descriptor systems

In this paper a new method for decentralized stabilization of a large-scale system in general form via state-feedback is presented. An appropriate descriptor system is defined for a large-scale system, such that the new system is in input-decentralized form. The interactions between the subsystems are considered as uncertainty. Sufficient conditions for stability of the closed-loop uncertain system are introduced. By appropriately assigning the eigenstructure of each isolated subsystem, these conditions are satisfied. This is accomplished by using the method suggested by Patton and Liu, such that the effects of the interconnections between the subsystems are compensated via the combination of genetic algorithms and gradient-based optimization.