Title :
Balanced Truncation for Discrete Time Markov Jump Linear Systems
Author :
Kotsalis, Georgios ; Rantzer, Anders
Author_Institution :
Autom. Control LTH, Lund Univ., Lund, Sweden
Abstract :
This technical note investigates the model reduction problem for mean square stable discrete time Markov jump linear systems. For this class of systems a balanced truncation algorithm is developed. The reduced order model is suboptimal, however the approximation error, which is captured by means of the stochastic gain, is bounded from above by twice the sum of singular numbers associated to the truncated states of each mode. Such a result allows rigorous simplification of the dynamics of each mode in an independent manner with respect to a metric which is relevant from a robust control point of view.
Keywords :
Markov processes; discrete time systems; linear systems; mean square error methods; reduced order systems; robust control; stochastic systems; approximation error; balanced truncation algorithm; mean square stable discrete time Markov jump linear system; model reduction problem; reduced order model; robust control; stochastic gain; Approximation error; Automatic control; Control system synthesis; Econometrics; Linear systems; Reduced order systems; Robust control; Signal processing; Signal synthesis; Stochastic processes; Jump linear systems (JLS´s); Markov jump linear systems (MJLS´s); linear time invariant (LTI) systems;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2010.2060241
