Mode-independent H2-control Of A Dc Motor Modeled As A Markov Jump Linear System

This brief presents a control strategy for Markov jump linear systems (MJLS) with no access to the Markov state (or mode). The controller is assumed to be in the linear state-feedback format and the aim of the control problem is to design a static mode-independent gain that minimizes a bound to the corresponding H2 -cost. This approach has a practical appeal since it is often difficult to measure or to estimate the actual operating mode. The result of the proposed method is compared with that of a previous design, and its usefulness is illustrated by an application that considers the velocity control of a DC motor device subject to abrupt failures that is modeled as an MJLS. © 1993-2012 IEEE.22519151919Dragan, V., Morozan, T., Stoica, A., H2 optimal control for linear stochastic systems (2004) Automatica, 40 (7), pp. 31103-31113. , JulCosta, O.L.V., Fragoso, M.D., Marques, R.P., (2005) Discrete-Time Markovian Jump Linear Systems, , New York NY USA: Springer-VerlagCosta, E.F., Vargas, A.N., Do Val, J.B.R., Quadratic costs and second moments of jump linear systems with general Markov chain (2011) Math. Control, Signals, Syst., 23 (1-3), pp. 141-157. , DecVargas, A.N., Furloni, W., Do Val, J.B.R., Second moment constraints and the control problem of Markov jump linear systems (2013) Numer. Linear Algebra Appl., 20 (2), pp. 357-368. , MarOliveira, R.C.L.F., Vargas, A.N., Do Val, J.B.R., Peres, P.L.D., Robust stability, H2 analysis and stabilisation of discrete-time Markov jump linear systems with uncertain probability matrix (2009) Int. J. Control, 82 (3), pp. 470-481. , JunDo Val, J.B.R., Costa, E.F., Stabilizability and positiveness of solutions of the jump linear quadratic problem and the coupled algebraic Riccati equation (2005) IEEE Trans. Autom. Control, 50 (5), pp. 691-695. , MayCosta, O.L.V., De Paulo, W.L., Indefinite quadratic with linear costs optimal control of Markov jump with multiplicative noise systems (2007) Automatica, 43 (4), pp. 587-597. , AprWu, L., Shi, P., Gao, H., Wang, C., H∞ filtering for 2D Markovian jump systems (2008) Automatica, 44 (7), pp. 1849-1858. , JulWu, L., Yao, X., Zheng, W.X., Generalized H2 fault detection for Markovian jumping two-dimensional systems (2012) Automatica, 48 (8), pp. 1741-1750. , AugWu, L., Su, X., Shi, P., Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems (2012) Automatica, 48 (8), pp. 1929-1933. , AugWu, L., Shi, P., Gao, H., State estimation and sliding-mode control of Markovian jump singular systems (2010) IEEE Trans. Autom. Control, 55 (5), pp. 1213-1219. , MayDo Val, J.B.R., Geromel, J.C., Gonçalves, A.P., The H2 control for jump linear systems: Cluster observations of the Markov state (2002) Automatica, 38 (2), pp. 343-349. , FebPeaucelle, D., Arzelier, D., An efficient numerical solution for H2 static output feedback synthesis (2001) Proc. Eur. Control Conf., Porto, Portugal, pp. 3800-3805. , SepArzelier, D., Peaucelle, D., Salhi, S., Robust static output feedback stabilization for polytopic uncertain systems: Improving the guaranteed performance bound (2003) Proc. 4th IFAC Symp. Robust Control des, pp. 425-430. , Milan, Italy, JunMehdi, D., Boukas, E.K., Bachelier, O., Static output feedback design for uncertain linear discrete time systems (2004) IMA J. Math. Control Inf., 21 (1), pp. 1-13. , MarMoreira, H.R., Oliveira, R.C.L.F., Peres, P.L.D., Robust H2 static output feedback design starting from a parameter-dependent state feedback controller for time-invariant discrete-time polytopic systems (2011) Opt. Control Appl. Methods, 32 (1), pp. 1-13. , JanAgulhari, C.M., Oliveira, R.C.L.F., Peres, P.L.D., LMI relaxations for reduced-order robust H∞ control of continuous-time uncertain linear systems (2012) IEEE Trans. Autom. Control, 57 (6), pp. 1532-1537. , JunCosta, O.L.V., Fragoso, M.D., Stability results for discrete-time linear systems with Markovian jumping parameters (1993) J. Math. Anal. Appl., 179 (1), pp. 154-178. , OctLee, J.-W., Dullerud, G.E., A stability and contractiveness analysis of discrete-time Markovian jump linear systems (2007) Automatica, 43 (1), pp. 168-173. , JanCosta, E.F., Do Val, J.B.R., Weak detectability and the linear-quadratic control problem of discrete-time Markov jump linear systems (2002) Int. J. Control, 75 (16-17), pp. 1282-1292Vargas, A.N., Costa, E.F., Do Val, J.B.R., On the control of Markov jump linear systems with no mode observation: Application to a DC motor device (2013) Int. J. Robust Nonlinear Control, 23 (10), pp. 1136-2115. , JulOstertag, E., (2011) Mono-and Multivariable Control and Estimation: Linear Quadratic and LMI Methods, , New York NY USA: Springer-VerlagVargas, A.N., Do Val, J.B.R., Average cost and stability of time-varying linear systems (2010) IEEE Trans. Autom. Control, 55 (3), pp. 714-720. , Ma