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This work strives for the issue of generalised dissipative asynchronous output feedback control for Markov jump repeated scalar non-linear systems with time-varying delay. The objective is to design an asynchronous output feedback controller, which ensures that the closed-loop system is generalised stochastically dissipative. Meanwhile, such an asynchronous controller covers not only the asynchronous controller but also the mode-independent one. By means of a stochastic analysis technique and a modified matrix decoupling method, sufficient conditions are given for deriving the desired controller. At length, an illustrative example is provided to demonstrate the availability of the presented approach.
This study is concerned about the quantitative exponential stability (QES) and stabilisation of discrete-time Markov jump systems with multiplicative noises. First, the defects of exponential stability in practical applications are analysed. Based on this analysis, a concept of the QES is given, and two stability criteria are derived. By utilising an auxiliary definition of general finite-time stability (GFTS), the relations among QES, GFTS and finite-time stability are established. Moreover, the quantitative exponential stabilisation is studied, and state feedback controller and the observer-based controller are designed. Subsequently, the relation between the states' upper bound and states' decay rate of considered systems is quantitatively shown by a searching method. Finally, an example is used to illustrate the effectiveness of the authors' obtained results.
This study addresses the estimation problem for discrete-time measurement-delay systems with multiplicative noise and Markov jump. First, the state equation is converted into two equations according to the geometric arguments and flexible transformations. Then, based on the reorganised innovation approach, the finite-horizon linear minimum mean-square-error estimator is derived in terms of two Riccati difference equations and two Lyapunov difference equations. Finally, under the assumptions of mean square stability of the system and ergodicity of the associated Markov chain, a sufficient condition for the existence of the infinite-horizon estimator is presented. We provide a numerical example to manifest the efficiency of the proposed approach.
This study is concerned with the finite-time energy-to-peak filtering problem for Markov jump repeated scalar non-linear systems with packet dropouts. The packet dropout phenomenon occurs in a random way and is modelled by a stochastic variable satisfying the Bernoulli distribution. The purpose of the study is to design a filter such that the resulting filtering error system is stochastically finite-time bounded, and a prescribed energy-to-peak performance level is achieved over a finite time interval. By using the mode-dependent diagonally dominant Lyapunov function approach, some strict linear matrix inequality-based conditions are established for the existence of an admissible filter, and a corresponding explicit parameterisation of such a filter is obtained. Finally, a numerical example with simulation is presented to demonstrate the effectiveness of our proposed approach.
