Abstract-This paper studies the problem of passivity-based asynchronous control for discrete-time Markov jump systems.The asynchronization phenomenon appears between the system modes and controller modes, which is described by a hidden Markov model. Accordingly, the resultant closed-loop system is named as a hidden Markov jump system. By utilizing the matrix inequality technique, three equivalent sufficient conditions are proposed to ensure the stochastic passivity of the hidden Markov jump systems. Based on the established conditions, the design of asynchronous controller, which covers synchronous controller and mode-independent controller as special cases, is addressed. A numerical example is given to demonstrate the effectiveness of the derived results.
This paper is concerned with the problem of analysis and optimisation of the inerter-based isolators based on a "uni-axial" single-degree-of-freedom isolation system. In the first part, in order to gain an in-depth understanding of inerter from the prospective of vibration, the frequency responses of both parallel-connected and series-connected inerters are analysed. In the second part, three other inerter-based isolators are introduced and the tuning procedures in both the H ∞ optimisation and the H 2 optimisation are proposed in an analytical manner. The achieved H 2 and H ∞ performance of the inerter-based isolators is superior to that achieved by the traditional dynamic vibration absorber (DVA) when the same inertance-tomass (or mass) ratio is considered. Moreover, the inerter-based isolators have two unique properties, which are more attractive than the traditional DVA: first, the inertance-to-mass ratio of the inerter-based isolators can easily be larger than the mass ratio of the traditional DVA without increasing the physical mass of the whole system; second, there is no need to mount an additional mass on the object to be isolated.
In this note, we address the reduced-order positive filtering problem of positive discrete-time systems under the performance. Commonly employed approaches, such as linear transformation and elimination technique, may not be applicable in general due to the positivity constraint of the filter. To cope with the difficulty, we first represent the filtering error system as a singular system by means of the system augmentation approach, which will facilitate the consideration of the positivity constraint. Two necessary and sufficient conditions are obtained in terms of matrix inequalities under which the filtering error system has a prescribed performance. Then, a necessary and sufficient condition is proposed for the existence of the desired positive filters, and an iterative linear matrix inequality (LMI) algorithm is presented to compute the filtering matrices, which can be easily checked by standard software. Finally, a numerical example to illustrate the effectiveness of the proposed design procedures is presented.
Index Terms-Discrete-time systems,filtering, linear matrix inequality, positive filtering, positive systems.
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