Causal and Strictly Causal Estimation for Jump Linear Systems: An LMI Analysis

Jump linear systems are linear state-space systems with random time variations driven by a finite Markov chain. These models are widely used in nonlinear control, and more recently, in the study of communication over lossy channels. This paper considers a general jump linear estimation problem of estimating an unknown signal from an observed signal, where both signals are described as outputs of a jump linear system. A bound on the minimum achievable estimation error in terms of linear matrix inequalities (LMIs) is presented, along with a simple jump linear estimator that achieves this bound. While previous analysis has considered only the strictly causal estimation problem, this work presents both strictly causal and causal solutions.