Bound Of Singular Perturbation Parameter Research Articles

Event-triggered consensus control for a class of two-time-scale multi-agent systems

The consensus control problem is studied for a class of two-time-scale multi-agent systems with the event-triggered mechanism (ETM). Under the communication topology, an event-based control scheme is proposed for each agent by utilising the relative measurement information between the agent itself and its neighbouring ones. A sampled-data-based ETM is constructed to decide when the current data-packet should be broadcast. This scheme takes full advantage of relative error-based ETM, and thus leading to a high efficiency of data transmissions. By virtue a novel singular perturbation parameter-dependent Lyapunov–Krasovskii functional, stability criteria and sufficient conditions for the consensus control algorithm and ETM are derived to guarantee that the state error dynamics is asymptotically stable. Furthermore, by using the proposed consensus controller design method, the ill-conditioned numerical issues caused by the two-time-scale property can also be avoided, and the upper bound of singular perturbation parameter is deduced explicitly. Finally, two convincing examples are employed to demonstrate the validity and effectiveness of the proposed transmission scheme and consensus control protocol.

Fault‐tolerant control of singularly perturbed systems with actuator faults and disturbances

SummaryThe article proposes several fault‐tolerant control (FTC) laws for singularly perturbed systems (SPS) with actuator faults and disturbances. One of the main challenges in this context is that the fast‐slow decomposition is not available for actuator faults and disturbances. In view of this, some conditions for the asymptotic stability of the closed‐loop dynamics are investigated by amending the composite Lyapunov approach. On top of this, a closed‐form expression of the upper bound of singular perturbation parameter (SPP) is provided. Moreover, we design several SPP‐independent composite FTC laws, which can be applied when this parameter is unknown. Finally, the chattering phenomenon is eliminated by using the continuous approximation technique. We also emphasize that, for linear SPSs, the FTC design can be formulated as a set of linear matrix inequalities, while the SPP upper bound can be obtained by solving a convex optimization problem. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.

Power System Transient Stability Study by Involving Higher Order Corrections in Improved Quadratic Lyapunov Function for Singular Perturbed Model of Synchronous Generator

The assessment of transient stability of multi-machine power system, in a post-fault scenario, is a very challenging task due to highly non-linear nature of the system equations. In this work, the physical concept of maximum relative acceleration of a machine at a fault scenario is related with the boundary of stability region. This approach is extended to develop a quadratic Lyapunov function using singular perturbed modelling. Unlike the conventional energy function methods, this Lyapunov function candidate is a more general energy function and has a decaying nature around an equilibrium point. Moreover, with higher order corrections, an improved Lyapunov function candidate is presented with simulation results of power system examples. The decaying nature of Lyapunov function candidate remains similar even without higher order corrections. However, the relevance of inclusion of higher order corrections is brought out in the cases of faults occurring at other than generator buses. Also, the upper bound of singular perturbation parameter in the model is within allowable limits and ensures the accuracy of results.

Dissipativity of Singularly Perturbed Lur’e Systems

The problem of singularly perturbed Lur’e systems is investigated in this brief. Two new storage functions are constructed to explore the dynamics of both the fast and slow models, as well as their interaction more efficiently. By using the merit of the proposed storage functions, some new $\varepsilon $ -uniformly strict dissipativity criteria in terms of well-conditioned linear matrix inequalities are derived. Moreover, a differential evolution algorithm is proposed to obtain the upper bound of singular perturbation parameter. The obtained results are theoretically and numerically less conservative than the existing results.

Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback

This paper focuses on the analysis and design of dissipativity-based fault-tolerant controller for discrete-time nonlinear Markov jump singularly perturbed systems (MJSPSs) which are based on Takagi–Sugeno fuzzy model. A novel strategy is proposed to improve the upper bound of singular perturbation parameter (SPP) ϵ, and the fault-tolerant design is also introduced, namely the susceptible property of systems is made full consideration, to ensure the specified performance of a system. The aim is to design an optimized slow state feedback controller such that the stability of MJSPSs is guaranteed even in faulty case, and the upper bound of the SPP ϵ is improved simultaneously. Utilizing Lyapunov functional technique, a sufficient condition for the existence of controller is shown. Last but not least, the control issue of a series DC motor model as an illustrated example is given to explain the availability of the presented design scheme.

Modulus consensus in a network of singularly perturbed systems with collaborative and antagonistic interactions

ABSTRACTThis paper addresses the modulus consensus in a network of singularly perturbed systems, all of which own multi-time scales characteristics. The interactions among the agents are collaborative and antagonistic interactions, and it can been modelled by a signed directed graph. Also, the effect of time-varying delay has been taken into account when modelling the agent dynamics. Based on singularly perturbed decomposition method, Kronecker product technique and the comparison principle, several sufficient conditions are presented under which networked singularly perturbed time-varying delay systems with collaborative and antagonistic interactions achieve modulus consensus. Moreover, the upper bound of singular perturbation parameter is deduced explicitly. Two simulation examples are presented to illustrate the validity of the proposed results.

Formula omitted] control design for fuzzy discrete-time singularly perturbed systems via slow state variables feedback: An LMI-based approach

This paper addresses the H ∞ control problem via slow state variables feedback for discrete-time fuzzy singularly perturbed systems. At first, a method of evaluating the upper bound of singular perturbation parameter ϵ with meeting a prescribed H ∞ performance bound requirement is given. Subsequently, two methods for designing H ∞ controllers via slow state variables feedback are presented in terms of solutions to a set of linear matrix inequalities (LMIs). In particular, one of them can be used to improve the upper bound of the singular perturbation parameter ϵ. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

Control Synthesis of Singularly Perturbed Fuzzy Systems

This paper considers the problem of designing stabilizing and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> controllers for nonlinear singularly perturbed systems described by Takagi-Sugeno fuzzy models with the consideration of the bound of singular perturbation parameter e. For the synthesis problem of simultaneously designing the bound of e and stabilizing or H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> controllers, linear matrix inequalities (LMI)- based methods are presented. For evaluating the upper bound of e subject to stability or a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance bound constraint for the resulting closed-loop system, sufficient conditions are developed, respectively. For the stabilizing and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> control synthesis without the consideration of improving the bound of e, new design methods are also given in terms of solutions to a set of LMIs. Examples are given to illustrate the efficiency of the proposed methods.

Formula omitted] control for fast sampling discrete-time singularly perturbed systems

This paper is concerned with the H ∞ control problem via state feedback for fast sampling discrete-time singularly perturbed systems. A new H ∞ controller design method is given in terms of solutions to linear matrix inequalities (LMIs), which eliminates the regularity restrictions attached to the Riccati-based solution. A method for evaluating the upper bound of singular perturbation parameter ϵ with meeting a prescribed H ∞ performance bound requirement is also given. Furthermore, the results are extended to robust controller design for fast sampling discrete-time singularly perturbed systems with polytopic uncertainties. Numerical examples are given to illustrate the validity of the proposed methods.

Robust H∞ control for standard discrete-time singularly perturbed systems

The state feedback H1 control problem for standard discrete-time singularly perturbed systems with polytopic uncertainties is considered. Two methods for designing H1 controllers are given in terms of solutions to a set of linear matrix inequalities, where one of them is with the con- sideration of improving the upper bound of singular perturbation parameter e. Moreover, a method of evaluating the upper bound of singular perturbation parameter e with meeting a prescribed H1 performance bound requirement is also given. Numerical examples are given to illustrate the effec- tiveness of the proposed methods.