Asynchronous control for two‐dimensional hidden Markovian jump systems with partly known mode observation conditional probabilities

Abstract

This study focuses on the asynchronous  ∞ control problem for two-dimensional discrete-time hidden Markovian jump systems where the mode observation conditional probability matrix is partly known. Considering the original system modes are invisible, the observed modes emitted from an observer serve as an alternative for stability analysis and controller design where a mode observation conditional probability matrix is constructed to characterize the emission between system modes and observed modes. Specially, only partly known information of the mode observation conditional probability matrix is accessible. With the introduction of the free-connection weighting matrices, the asymptotic mean square stability criterion is firstly derived based on Lyapunov method. This introduction provides a further degree of relaxation and less conservatism is therefore achieved. Secondly, we present synthesis conditions for asynchronous  ∞ state feedback controller design given in terms of a set of interconnected linear matrix inequalities. Moreover, cluster concept based on the partitions of observed modes is adopted which helps to decrease the number of controllers and simplify the design complexity. A numerical example, regarding the cases with and without clustering of the observed modes, is presented to illustrate the effectiveness of the proposed method.

Event‐triggered asynchronous filtering for networked fuzzy non‐homogeneous Markov jump systems with dynamic quantization

“…On the other hand, non‐homogeneous MJSs, that is, MJSs with time‐varying MTPM, are more general and challenging. Several fundamental techniques include, the piecewise homogeneous approach which assumes the split of the MTPM into piecewise time‐invariant ones, 2,9 the polytopic approach based on the polynomial cumulative form of the time‐varying MTPM, 10‐13 the dwell‐time switching approach where the MTPM depends on the operation time, 14 and the norm‐bounded uncertainties approach designed for the norm‐bounded MTPM 15,16 . Based on these techniques, achievements have been made to address issues in non‐homogeneous MJSs including stability analysis, 10,14 model reduction, 11 filter design, 12,13 and so forth.…”