This paper presents a new detectability concept for discrete-time Markov jump linear systems with finite Markov state, which generalizes the MS-detectability concept found in the literature. The new sense of detectability can similarly assure that the solution of the coupled algebraic Riccati equation associated to the quadratic control problem is a stabilizing solution. In addition, the paper introduces a related observability concept which also generalizes previous concepts. Tests for detectability or observability are derived from the corresponding definitions, that can be performed in a finite number of steps. An illustrative example is included to show that a system may be detectable in the new sense but not in the MS sense.3 23552360Anderson, B.D.O., Moore, J.B., Detectability and stabilizability of time-varying discrete-time linear systems (1981) SIAM Journal on Control and Optimization, 19 (1), pp. 20-32Costa, O.L.V., Do Val, J.B.R., Geromel, J.C., A convex programming approach to h2 control of discrete-time Markovian jump linear systems (1997) Int. J. Control, 66 (4), pp. 557-579Costa, O.L.V., Fragoso, M.D., Stability results for discrete-time linear systems with Markovian jumping parameters (1993) J. Math. Analysis and Applications, 179, pp. 154-178Costa, O.L.V., Fragoso, M.D., Discrete-time LQ-optimal control problems for infinite Markov jump parameter systems (1995) IEEE Trans. Auto. Control, 40 AC, pp. 2076-2088De Farias, D.P., Geromel, J.C., Do Val, J.B.R., Costa, O.L.V., Output feedback control of Markov jump linear systems in continuous-time IEEE Trans. Auto. Control, , to appearDo Val, J.B.R., Başar, T., Receding horizon control of jump linear systems and a macroeconomic policy problem (1999) Journal of Economic Dynamics & Control, 23, pp. 1099-1131Do Val, J.B.R., Geromel, J.C., Costa, O.L.V., Solutions for the linear quadratic control problem of Markov jump linear systems (1999) Journal of Optimization Theory and Applications, 103, pp. 283-311Hager, W.W., Horowitz, L.L., Convergence and stability properties of the discrete Riccati operator equation and the associated optimal control and filtering problems (1976) SIAM Journal on Control and Optimization, 14 (2), pp. 295-312Ji, Y., Chizeck, H.J., Controlability, stabilizability and continuous time Markovian jump linear quadratic control (1990) IEEE Trans. Auto. Control, 35 (7), pp. 777-788Ji, Y., Chizeck, H.J., Jump linear quadratic Gaussian control: Steady-state solution and testable conditions (1990) Control Theory and Advanced Technology, 6 (3), pp. 289-319Ji, Y., Chizeck, H.J., Feng, X., Loparo, K.A., Stability and control of discrete-time jump linear systems (1991) Control Theory and Advanced Technology, 7 (2), pp. 247-269Pan, G., Bar-Shalom, Y., Stabilization of jump linear Gaussian systems without mode observations (1996) Int. J. Control, 64 (4), pp. 631-661