H∞ dynamic output feedback control of power systems with electric vehicles

This paper presents a H∞ dynamic output feedback control scheme for load frequency control (LFC) of interconnected power systems with multiple input timedelays. In this study, electric vehicles (EVs) are participated in the LFC to support reheated thermal power units to rapidly suppress load and frequency fluctuations. A mathematical model of an interconnected power system is first introduced. This model takes into consideration of the different time delays in control inputs; specifically the communication/information delays between the control center and the fleet of EVs. We then derive stabilization conditions in terms of feasible linear matrix inequalities (LMIs) for the proposed system and develop an effective algorithm to parameterize H∞ controllers ensuring stability of the closed-loop system with H∞ performance. Extensive simulations are given to show the effectiveness of the proposed control method.

Stability analysis of two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities

This paper is concerned with the problem of stochastic stability analysis of discrete-time two-dimensional (2-D) Markovian jump systems (MJSs) described by the Roesser model with interval time-varying delays. The transition probabilities of the jumping process/Markov chain are assumed to be uncertain, that is, they are not exactly known but can be estimated. A Lyapunov-like scheme is first extended to 2-D MJSs with delays. Based on some novel 2-D summation inequalities proposed in this paper, delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities (LMIs) which can be computationally solved by various convex optimization algorithms. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.

Observer design for one-sided Lipschitz discrete-time systems subject to delays and unknown inputs

In this paper, we address the problem of observer design for a class of nonlinear discrete-time systems in the presence of delays and unknown inputs. The nonlinearities studied in this work satisfy the one-sided Lipschitz and quadratically inner-bounded conditions which are more general than the traditional Lipschitz conditions. Both H∞ observer design and asymptotic observer design with reduced-order are considered. The designs are novel compared to other relevant nonlinear observer designs subject to time delays and disturbances in the literature. In order to deal with the time-delay issue as well as the bilinear terms which usually appear in the problem of designing observers for discrete-time systems, several mathematical techniques are utilized to deduce observer synthesis conditions in the linear matrix inequalities form. A numerical example is given to demonstrate the effectiveness and high performance of our results.

Integration of electric vehicles for load frequency output feedback H ∞ control of smart grids

This study considers a novel application of electric vehicles (EVs) to quickly help reheated thermal turbine units to provide the stability fluctuated by load demands. A mathematical model of a power system with EVs is first derived. This model contains the dynamic interactions of EVs and multiple network-induced time delays. Then, a dynamic output feedback H∞ controller for load frequency control of power systems with multiple time delays in the control input is proposed. To address the multiple time delays issue, a refined Jensen-based inequality, which encompasses the Jensen inequality, is used to derive less conservative synthesis conditions in terms of tractable linear matrix inequalities. A procedure is given to parameterise an output feedback controller to guarantee stability and H∞ performance of the closed-loop system. Extensive simulations are conducted to validate the proposed control method.

Exponential stabilization of non-autonomous delayed neural networks via Riccati equations

This paper concerns with the problem of exponential stabilization for a class of non-autonomous neural networks with mixed discrete and distributed time-varying delays. Two cases of discrete time-varying delay, namely (i) slowly time-varying; and (ii) fast time-varying, are considered. By constructing an appropriate Lyapunov-Krasovskii functional in case (i) and utilizing the Razumikhin technique in case (ii), we establish some new delay-dependent conditions for designing a memoryless state feedback controller which stabilizes the system with an exponential convergence of the resulting closed-loop system. The proposed conditions are derived through solutions of some types of Riccati differential equations. Applications to control a class of autonomous neural networks with mixed time-varying delays are also discussed in this paper. Some numerical examples are provided to illustrate the effectiveness of the obtained results.

Reachable sets bounding for generalized neural networks with interval time-varying delay and bounded disturbances

This paper deals with the problem of finding outer bound of forwards reachable sets and interbound of backwards reachable sets of generalized neural network systems with interval nondifferentiable time-varying delay and bounded disturbances. Based on constructing a suitable Lyapunov–Krasovskii functional and utilizing some improved Jensen integral-based inequalities, two sufficient conditions are derived for the existence of: (1) the smallest possible outer bound of forwards reachable sets and (2) the largest possible interbound of backwards reachable sets. These conditions are delay dependent and in the form of matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. Three numerical examples with simulation results are provided to demonstrate the effectiveness of our results.

Static output feedback frequency stabilization of time-delay power systems with coordinated electric vehicles state of charge control

In this paper, for the first time, electric vehicles are used for both the primary and secondary frequency controls to support power plants to rapidly suppress fluctuations in the system frequency due to load disturbances. Via networked control and wide-area communication infrastructures, multiple interval time-varying delays exist in the communication channels between the control center, power plant, and an aggregation of electric vehicles. By coordinating batteries’ state of charge control, the behaviors of the vehicle owners and the uncertainties imposed by the changes of the batteries’ state of charge are taken intoconsideration. A power system model incorporating multiple time-varying delays and uncertainties is first proposed. Then, a robust static output feedback frequency controller is designed to guarantee the resulting closed-loop system stable with an H∞ attenuation level. By utilizing a novel integral inequality, namely refined-Jensen inequality, and an improved reciprocally convex combination, the design conditions are formulated in terms of tractable linear matrix inequalities which can be efficiently solved by various computational tools. The effectiveness of the proposed control scheme is verified by extensive simulations.

Partial state estimation for linear systems with output and input time delays.

This paper deals with the problem of partial state observer design for linear systems that are subject to time delays in the measured output as well as the control input. By choosing a set of appropriate augmented Lyapunov-Krasovskii functionals with a triple-integral term and using the information of both the delayed output and input, a novel approach to design a minimal-order observer is proposed to guarantee that the observer error is ε-convergent with an exponential rate. Existence conditions of such an observer are derived in terms of matrix inequalities for the cases with time delays in both the output and input and with output delay only. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality and effectiveness of the proposed observer.

Stability of two-dimensional Roesser systems with time-varying delays via novel 2D finitesum inequalities

This study considers the problem of stability analysis of discrete-time two-dimensional (2D) Roesser systems with interval time-varying delays. New 2D finite-sum inequalities, which provide a tighter lower bound than the existing ones based on 2D Jensen-type inequalities, are first developed. Based on an improved Lyapunov-Krasovskii functional, the newly derived inequalities are then utilised to establish delay-range-dependent linear matrix inequality-based stability conditions for a class of discrete time-delay 2D systems. The effectiveness of the obtained results is demonstrated by numerical examples.

An explicit criterion for finite-time stability of linear nonautonomous systems with delays

In this paper, the problem of finite-time stability of linear nonautonomous systems with time-varying delays is considered. Using a novel approach based on some techniques developed for linear positive systems, we derive new explicit conditions in terms of matrix inequalities ensuring that the state trajectories of the system do not exceed a certain threshold over a pre-specified finite time interval. These conditions are shown to be relaxed for the Lyapunov asymptotic stability. A numerical example is given to illustrate the effectiveness of the obtained result.

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MA167exam00

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Exponential stabilization for state and input delay systems via output feedback

This paper considers the exponential stabilization problem via static and dynamic output feedback controllers of linear systems with a time delay in both the state and input. By using a change of the state variable and combining with the Lyapunov-Krasovskii method, new sufficient conditions for exponential stabilization via static and dynamic output feedback controllers are proposed. The conditions are expressed in terms of matrix inequalities but with only one parameter needs to be tuned and therefore can be efficiently solved by incorporating an one-dimensional search method into the Matlab’s LMI toolbox. Two numerical examples are provided to illustrate the obtained results.