A Spectrum Characterization of Feedback Capability for Unknown Markovian Jump Linear Systems

This paper is concerned with the capability of adaptation for linear time-varying systems with unknown parameters modeled as a hidden Markov chain. A concise spectrum characterization of feedback capability for unknown Markovian jump linear stochastic systems is provided based on the work of Xue and Guo (2001), which avoids the use of matrix solutions for a set of algebraic coupled Riccati-like equations. From this new characterization, it is not difficult to see that the key inherent factor in characterizing the capability of adaptation is the information uncertainty, coupled with the model complexity by the dispersion of the coefficient matrices of Markovian jump linear systems.