Control For Two-dimensional Discrete-time Hidden Markovian Jump Systems

Markovian jump systems have unparalleled advantages in modeling a family of practical dynamic systems which are susceptible to sudden component failures or ran-dom changes in system structure and parameters.For the reason that Markovian jump systems have widespread applications in communication networks,financial invest-ment,aeronautics and astronautics,industrial machinery manufacturing and so on,this subject has generated a flurry of interest and highly attention by many scholars,and in the sense of theory and practice,systematically studied this subject is of great paramount importance.Differing from traditional non-jump systems,the characteristics of discrete-time Markovian jump systems lie in two key aspects:system modes and mode transition probability matrix.So far,surrounding these two characteristics,the related achieve-ments about Markovian jump systems have reached a relatively mature level,and most of the research results are established on the hypothesis that the accurate information of system modes is completely available.However,in real applications acquiring the information of system modes is impossible even highly cost.Naturally,the analysis of the scenario of system mode is invisible will have to face great challenges but of great significance.Together with the system mode and the observed mode obtained by the observer structure form a hidden Markov chain.The certain emission proba-bilities between system modes and the observed modes are characterized by the mode observation conditional probability matrix,in this sense,the jump systems containing the hidden Markov chain is called hidden Markovian jump systems(HMJSs).In ad-dition,two-dimensional discrete-time systems,whose system information propagation takes place in two independent dimensions,have attract much more attention because of the widespread applications of large-scale systems.In this dissertation,consider-ing the two-dimensional discrete-time system established upon the Roesser model,and by virtue of hidden Markov model,the two-dimensional hidden Markovian jump sys-tems is taken as the research subject,the system stability and H? control problems are studied under the condition that the mode observation conditional probability matrix is partly unknown.The research contents are summarized as follows:·Stability and stabilization problems for two-dimensional discrete-time hidden Marko-vian jump systems are investigated.By virtue of hidden Markov model,the two-dimensional hidden Markovian jump systems model under the condition that sys-tem modes and observed modes are asynchronous is firstly established,and the mode observation conditional probability matrix is assumed to be partly known.Based on constructed system-mode-dependent Lyapunov function,and divided the mode observation conditional probability matrix into known and unknown two parts to further analyze and synthesize,the sufficient condition that guaran-teed the underlying system asymptotic mean square stability criterion is estab-lished.Furthermore,by introducing slack variables,the asynchronous controller which can ensure the stability of the closed-loop two-dimensional system is de-signed in the form of a set of inter-connected linear matrix inequalities.Finally,a simulation example which takes the heating process as the background verifies the correctness and validity of the theoretical analysis results.·Asynchronous H? state feedback control and the clustering of observed modes problems for two-dimensional hidden Markovian jump systems are studied.Firstly,the two-dimensional hidden Markovian jump system model is established under the existence of external disturbance input.Then,with the introduction of system performance index,a sufficient condition guarantees the resultant system pos-sess both asymptotic mean square stability and prescribed H? noise attenuation performance.In the meanwhile,the introduction of free-connection weighting matrix reduces the conservatism of the obtained results.Moreover,a novel con-cept of clustering of observed modes is proposed,so that the computational bur-den is greatly reduced and the complexity of design of asynchronous controllers is therefore simplified.Finally,the numerical simulation of Darboux equation proves that the proposed asynchronous H? state feedback controller design is effective.