Robust Control For Markov Jump Linear Systems

Fault-prone dynamic systems may experience abrupt changes in their structures and parameters, which are often caused by component failures or repairs, changing subsystem interconnections, abrupt environmental disturbances, and so on. Such physical systems have been modeled as Markov jump linear systems (or Markovian switching system). This class of systems has attracted much attention from the model first introduced in 1961, and many results have been obtained in the literature.For the essential difference between Markov jump system and the usual linear system with only one mode (without jump or switching), there is more difficulty and challenge for the investigation on Markov jump linear systems.In the light of the recent work on Markov jump linear systems, and the result of robust control for linear systems with one mode, the dissertation provides some results on robust control, H_∞ control, time-weighted H₂ control, time-weighted H₂ model reduction and H_∞ model reduction. The main results obtained in this dissertation are as follows:a) The robust stabilization problem for Markov jump linear systems with input delay is studied. The input delay here is time-varying and mode-dependent, and is constant for each mode. Sufficient condition for Markov jump linear system to be robust stabilization is given, and the corresponding memory controller is designed. It is noticed that the proposed method can also be applied to linear systems with one mode. The simulation example shows that our approach has less conservativeness.b) Based on the H₂ norm and the time-weighted performance index, the time-weighted H₂ norm is introduced for the first time, and the computation formula is also obtained. Necessary and sufficient condition for Markov jump linear system to be mean square stable and satisfying the given time-weighted H₂ norm at the same time. The time-weighted H-2 controller is also designed through an iterative algorithm.c) According to the analysis of the time-weighted H₂ performance, the optimal time-weighted H₂ model reduction problem for Markov jump linear systems is considered. That is, for a given mean square stable Markov jump system, our aim is to find a mean square stable jump system with lower order such that the...