Stability of a random Riccati equation with Markovian binary switching

We consider the stability of a random Riccati equation arising from Kalman filtering with observation losses. More specifically, we are concerned with the boundedness of the solution of a random Riccati difference equation with a Markovian binary jump parameter. A sufficient condition for the peak covariance stability is obtained which has a simpler form and is shown to be less conservative in some cases than a very recent result in existing literature. Furthermore, we show that a known sufficient condition is also necessary when the observability index of the system equals one. In addition, we give some conditions under which the covariance matrix is bounded for a special case or unbounded in the usual sense. The equivalence between the peak covariance stability and the usual covariance stability is established for systems with the observability index of one and i.i.d. observation losses.