Stability and disturbance attenuation for a switched Markov jump linear system
For control theorists, this offers a rigorous stability and performance analysis framework for a broader class of switching systems.
The paper provides necessary and sufficient conditions for uniform stochastic stability and disturbance attenuation in Markov jump linear systems with unknown time-inhomogeneous transition probabilities, expressed as solvable linear matrix inequalities.
We address a class of Markov jump linear systems that are characterized by the underlying Markov process being time-inhomogeneous with a priori unknown transition probabilities. Necessary and sufficient conditions for uniform stochastic stability and uniform stochastic disturbance attenuation are reported. In both cases, conditions are expressed as a set of finite-dimensional linear matrix inequalities that can be solved efficiently.