New methods for mode-independent robust control of Markov jump linear systems

This paper treats the H2 and H∞ controls of linear systems with Markov jump disturbances, via new design methods based on linear matrix inequalities (LMIs). The proposed techniques are especially tailored to the scenario where the jump process cannot be measured, and apply to homogeneous Markov chains of any structure. In the scenario of polytopic uncertainty affecting the system matrices, new uncertainty-dependent methods are introduced for the design of robust controllers. Several numerical examples illustrate situations where the proposed techniques are less conservative than the ones found in the literature.

[1]  Guillaume Ducard,et al.  Fault-tolerant Flight Control and Guidance Systems: Practical Methods for Small Unmanned Aerial Vehicles , 2009 .

[2]  R. P. Marques,et al.  Mixed H2/H∞-control of discrete-time Markovian jump linear systems , 1998, IEEE Trans. Autom. Control..

[3]  Vasile Dragan,et al.  Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems , 2009 .

[4]  James Lam,et al.  Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities , 2008, IEEE Transactions on Automatic Control.

[5]  M. C. D. Oliveiraa,et al.  A new discrete-time robust stability condition ( , 1999 .

[6]  Raja Sengupta,et al.  An H/sub /spl infin// approach to networked control , 2005, IEEE Transactions on Automatic Control.

[7]  P. Caines,et al.  On the Adaptive Control for Jump Parameter Systems viaNonlinear Filtering , 1995 .

[8]  Marcelo D. Fragoso,et al.  A separation principle for the H2-control of continuous-time infinite markov jump linear systems with partial observations , 2007, 2007 European Control Conference (ECC).

[9]  Huijun Gao,et al.  H∞ Fuzzy Control of Nonlinear Systems Under Unreliable Communication Links , 2009, IEEE Trans. Fuzzy Syst..

[10]  Alexandre Trofino,et al.  Mode-Independent ${\cal H}_{\infty}$ Filters for Markovian Jump Linear Systems , 2006, IEEE Transactions on Automatic Control.

[11]  Alim P. C. Gonçalves,et al.  H2 and Hoo Filtering of Discrete-Time Markov Jump Linear Systems through Linear Matrix Inequalities , 2008 .

[12]  M. Fragoso,et al.  Stability Results for Discrete-Time Linear Systems with Markovian Jumping Parameters , 1993 .

[13]  Alim P. C. Gonçalves,et al.  H∞ robust and networked control of discrete-time MJLS through LMIs , 2012, J. Frankl. Inst..

[14]  Alessandro N. Vargas,et al.  On the control of Markov jump linear systems with no mode observation: application to a DC Motor device , 2013 .

[15]  M. Fragoso,et al.  Continuous-Time Markov Jump Linear Systems , 2012 .

[16]  Shaoyuan Li,et al.  Transmission probability condition for stabilisability of networked control systems , 2010 .

[17]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[18]  C.E. de Souza,et al.  Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems , 2006, IEEE Transactions on Automatic Control.

[19]  Alim P. C. Gonçalves,et al.  Optimal H2 and H∞ Mode-Independent Control for Generalized Bernoulli Jump Systems , 2014 .

[20]  Marcelo D. Fragoso,et al.  A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters , 2010, IEEE Transactions on Automatic Control.

[21]  R. P. Marques,et al.  Discrete-Time Markov Jump Linear Systems , 2004, IEEE Transactions on Automatic Control.

[22]  Carlos E. de Souza,et al.  Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems , 2006, IEEE Transactions on Automatic Control.

[23]  Oswaldo Luiz V. Costa,et al.  Stationary filter for linear minimum mean square error estimator of discrete-time Markovian jump systems , 2002, IEEE Trans. Autom. Control..

[24]  Daniel E. Quevedo,et al.  Packetized Predictive Control of Stochastic Systems Over Bit-Rate Limited Channels With Packet Loss , 2011, IEEE Transactions on Automatic Control.

[25]  R. Elliott,et al.  Adaptive control of linear systems with Markov perturbations , 1998, IEEE Trans. Autom. Control..

[26]  Alim P. C. Gonçalves,et al.  ℋ 2 filtering of discrete-time Markov jump linear systems through linear matrix inequalities , 2008, Int. J. Control.

[27]  Ricardo C. L. F. Oliveira,et al.  Mode-Independent ${\cal H}_{2}$ -Control of a DC Motor Modeled as a Markov Jump Linear System , 2014, IEEE Transactions on Control Systems Technology.

[28]  J. Geromel,et al.  A new discrete-time robust stability condition , 1999 .

[29]  M. Fragoso,et al.  On a partially observable LQG problem for systems with Markovian jumping parameters , 1988 .

[30]  Alim P. C. Gonçalves,et al.  Optimal and mode-independent filters for generalised Bernoulli jump systems , 2015, Int. J. Syst. Sci..

[31]  Raja Sengupta,et al.  A bounded real lemma for jump systems , 2003, IEEE Trans. Autom. Control..

[32]  Wei-Yong Yan,et al.  Stability robustness of networked control systems with respect to packet loss , 2007, Autom..

[33]  L. Ghaoui,et al.  Robust state-feedback stabilization of jump linear systems , 1996 .

[34]  Marcelo D. Fragoso,et al.  New methods for mode-independent robust control of Markov jump linear systems , 2014, CDC.

[35]  Marcelo D. Fragoso,et al.  A new look at the robust control of discrete-time Markov jump linear systems* , 2016, Int. J. Control.

[36]  J. Geromel,et al.  A Convex Programming Approach to the H2-Control of Discrete-Time Markovian Jump Linear Systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[37]  Nei C. S. Rocha,et al.  Stationary filter for continuous-time Markovian jump linear systems , 2004, CDC.

[38]  Ricardo C. L. F. Oliveira,et al.  Robust stability, ℋ2 analysis and stabilisation of discrete-time Markov jump linear systems with uncertain probability matrix , 2009, Int. J. Control.

[39]  J.C. Geromel,et al.  ${\cal H}_{\infty}$ Filtering of Discrete-Time Markov Jump Linear Systems Through Linear Matrix Inequalities , 2009, IEEE Transactions on Automatic Control.

[40]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[41]  V. Dragan,et al.  Mathematical Methods in Robust Control of Linear Stochastic Systems , 2006 .

[42]  Alim P. C. Gonçalves,et al.  The H2-control for jump linear systems: cluster observations of the Markov state , 2002, Autom..

[43]  Marcelo D. Fragoso,et al.  On the Filtering Problem for Continuous-Time Markov Jump Linear Systems with no Observation of the Markov Chain , 2011, Eur. J. Control.

[44]  Marcelo D. Fragoso,et al.  A Small Random Perturbation Analysis of a Partially Observable LQG Problem for Systems with Markovian Jumping Parameters , 1990 .

[45]  O. L. V. Costa,et al.  Finite horizon quadratic optimal control and a separation principle for Markovian jump linear systems , 2003, IEEE Trans. Autom. Control..

[46]  Weidong Zhang,et al.  H ∞ Estimation for Stochastic Time Delays in Networked Control Systems by Partly Unknown Transition Probabilities of Markovian Chains. , 2013, Journal of dynamic systems, measurement, and control.

[47]  R. P. Marques,et al.  Mixed H2/H∞-control of discrete-time Markovian jump linear systems , 1998, IEEE Trans. Autom. Control..

[48]  James Lam,et al.  On robust stabilization of Markovian jump systems with uncertain switching probabilities , 2005, Autom..

[49]  Oswaldo L. V. Costa.  MIXED H 2 / H ~ CONTROL OF DISCRETE-TIME MARKOVIAN JUMP LINEAR SYSTEMS * , 1996 .