H2 Filtering Of Discrete-time Markov Jump Linear Systems Through Linear Matrix Inequalities

This paper addresses the H2 filtering design problem of discrete-time Markov jump linear systems. First, under the assumption that the Markov parameter is measured, the main contribution is on the LMI characterisation of all filters such that the estimation error remains bounded by a given H2 norm level, yielding the complete solution of the mode-dependent filtering design problem. Based on this result, a robust filter design to deal with convex bounded parameter uncertainty is considered. Second, from the same LMI characterisation, a design procedure for mode-independent filtering design is proposed. Some examples are solved for illustration and comparison.81812211231Anderson, B.D.O., Moore, J.B., (1979) Optimal Filtering, , Englewood Cliffs, NJ: Prentice HallBlair Jr, W.P., Sworder, D.D., Feedback Control of a Class of Linear Discrete Systems with Jump Parameters and Quadratic Cost Criteria (1975) International Journal of Control, 21, pp. 833-841Boyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , Philadelphia, PA: SIAMCosta, O.L.V., do Val, J.B.R., Geromel, J.C., A Convex Programming Aproach to H2 Control of Discrete-time Markovian Linear Systems (1997) International Journal of Control, 66, pp. 557-579Costa, O.L.V., Fragoso, M.D., Stability Results for Discrete-time Linear Systems with Markovian Jump Parameters (1993) Journal of Mathematical Analysis and Applications, 179, pp. 154-178Costa, O.L.V., Marques, R.P., Mixed H 2/H∞-control of Discrete-time Markovian Jump Linear Systems (1998) IEEE Transactions on Automatic Control, 43, pp. 95-100Costa, O.L.V., Guerra, S., Stationary Filter for Linear Minimun Mean Square Error Estimator of Discrete-time Markovian Jump Systems (2002) IEEE Transactions on Automatic Control, 47, pp. 1351-1356Costa, O.L.V., Guerra, S., Robust Linear Filtering for Discrete-time Hybrid Markov Linear Systems (2002) International Journal of Control, 75, pp. 712-727Costa, O.L.V., Tuesta, E.F., H 2-Control and the Separation Principle for Discrete-time Markovian Jump Linear Systems (2004) Mathematics of Control, Signals and Systems, 16, pp. 320-350de 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 (2000) IEEE Transactions on Automatic Control, 45, pp. 944-949de Souza, C.E., Mode-independent H∞ Control of Discrete-time Markovian Jump Linear Systems (2005) Proceedings of the 16th IFAC World Congress, , Prague, Czech Republicde Souza, C.E., A mode-independent H∞ Filter Design for Discrete-time Markovian Jump Linear Systems (2003) Proceedings of the 42nd IEEE Conference on Decision and Control, 3, pp. 2811-2816do Val, J.B.R., Geromel, J.C., Gonçalves, A.P.C., The H2-control for Jump Linear Systems: Cluster Observations of the Markov State (2002) Automatica, 38, pp. 343-349Ji, Y., Chizeck, H.J., Jump Linear Quadratic Control: Steady State Solution and Testable Conditions (1990) Control Theory and Advanced Technology, 5, 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, pp. 247-270Ji, Y., Chizeck, H.J., Controllability, Observability and Discrete-time Markovian Jump Linear Quadratic Control (1988) International Journal of Control, 48, pp. 481-498Seiler, P., Sengupta, R., An H∞ Approach to Networked Control (2005) IEEE Transactions on Automatic Control, 50, pp. 356-364Sworder, D.D., Rogers, R.O., An LQ-Solution to a Control Problem Associated with a Solar Thermal Central Receiver (1983) IEEE Transactions on Automatic Control, 28, pp. 971-97