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Original Articles

H2 optimal control for a wide class of discrete-time linear stochastic systems

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Pages 1029-1049 | Received 18 Apr 2008, Accepted 04 Apr 2009, Published online: 23 Oct 2009

References

  • Abou-Kandil , H , Freiling , G and Jank , G . 1995 . On the Solution of Discrete-Time Markovian Jump Linear Quadratic Control Problems . Automatica , 32 : 765 – 768 .
  • Basin , M , Perez , J and Calderon-Alvarez , D . 2008 . Optimal Filtering for Linear Systems over Polynomial Observations . International Journal of Innovative Computing, Information and Control , 4 ( 2 ) : 313 – 320 .
  • Basin , M , Sanchez , E and Martinez-Zuniga , R . 2007 . Optimal Linear Filtering for Systems with Multiple State and Observation Delays . International Journal of Innovative Computing, Information and Control , 3 ( 5 ) : 1309 – 1320 .
  • Blair , WP and Sworder , DD . 1975 . Feedback Control of a Class of Linear Discrete Systems with Jump Parameters and Quadratic Cost Criteria . International Journal of Control , 21 : 833 – 841 .
  • Boukas , EK . 1993 . Control of Systems with Controlled Jump Markov Disturbances . Control Theory and Advanced Technology , 9 : 577 – 595 .
  • Chizeck , HJ , Willsky , AS and Castanon , D . 1986 . Discrete-Time Markovian-Jump Linear Quadratic Optimal Control . International Journal of Control , 43 : 213 – 221 .
  • Costa , OLV . 1994 . Linear Minimum Mean Square Error Estimation for Discrete-Time Markovian Jump Linear Systems . IEEE Transactions on Automatic Control , 39 : 1685 – 1689 .
  • Costa , OLV , do Val , JBR and Geromel , JC . 1999 . Continuous Time State Feedback H 2 Control of Markovian Jump Linear Systems via Convex Analysis . Automatica , 35 : 259 – 268 .
  • Costa , EF and do Val , JBR . 2004 . An Algorithm for Solving a Perturbed Algebraic Riccati Equation . European Journal of Control , 10 : 576 – 580 .
  • Costa , OLV , Fragoso , MD and Marques , RP . 2005 . Discrete-time Markov jump linear systems , London : Springer .
  • Costa , OLV and Marques , RP . 1998 . Mixed H 2/H ∞ Control of Discrete Time Markovian Jump Linear Systems . IEEE Transactions on Automatic Control , 43 : 95 – 100 .
  • Costa , OLV and Marques , RP . 2000 . Robust H 2-Control for Discrete-Time Markovian Jump Linear Systems . International Journal of Control , 73 : 11 – 21 .
  • Costa , OLV and Tuesta , EF . 2004 . H 2-Control and the Separation Principle for Discrete-time Markovian Jump Linear Systems . Mathematical of Control Signals and Systems , 16 : 320 – 350 .
  • DaPrato , G and Ichikawa , A . 1990 . Quadratic Control for Linear Time Varying Systems . SIAM Journal of Control Optimization , 28 : 359 – 381 .
  • De Farias , DP , Geromel , JC , do Val , JBR and Costa , OLV . 2000 . Output Feedback Control of Markov Jump Linear Systems in Continuous-time . IEEE Transactions on Automatic Control , 45 : 944 – 949 .
  • Doob , JL . 1967 . Stochastic processes , New-York : Wiley .
  • Doyle , JC , Glover , K , Khargonekaar , PP and Francis , BA . 1989 . State Space Solutions to Standard H 2 and H ∞ Control Problems . IEEE Transactions on Atomatic Control , 34 : 831 – 847 .
  • Dragan , V and Morozan , T . 2006a . Exponential Stability for Discrete Time Linear Equations Defined by Positive Operators . Integral Equations and Operator Theory , 54 : 465 – 493 .
  • Dragan , V and Morozan , T . 2006b . Mean Square Exponential Stability for Some Stochastic Linear Discrete Time Systems . European Journal of Control , 12 : 373 – 395 .
  • Dragan , V and Morozan , T . 2008a . Exponential Stability in Mean Square for a General Class of Discrete-Time Linear Stochastic Systems . Stochastic Analysis and Applications , 26 : 495 – 525 .
  • Dragan , V and Morozan , T . 2008b . Discrete-Time Riccati Type Equations and the Tracking Problem . ICIC Express Letters , 2 ( 2 ) : 109 – 116 .
  • Dragan , V and Morozan , T . 2008c . The Linear Quadratic Optimisation Problem for a Class of Discrete-Time Stochastic Linear Systems . International Journal of Innovative Computing, Information and Control , 4 ( 9 ) : 2127 – 2137 .
  • Dragan , V and Morozan , T . 2009 . A Class of Discrete Time Generalised Riccati Equations . Journal of Difference Equations and Applications , in press
  • Dragan , V , Morozan , T and Halanay , A . 1992 . Optimal Stabilising Compensator for Linear Systems with State Dependent Noise . Stochastic Analysis and Applications , 10 : 557 – 572 .
  • Dragan , V , Morozan , T and Stoica , AM . 2004 . H 2-Optimal Control for Linear Stochastic Systems . Automatica , 40 : 1103 – 1113 .
  • Dragan , V , Morozan , T and Stoica , AM . 2006 . “ Mathematical Methods in Robust Control of Linear Stochastic Systems ” . In Mathematical Concepts and Methods in Science and Engineering , Edited by: Angelo , Miele . Vol. 50 , New York : Springer .
  • Fragoso , MD . 1988 . Discrete-Time Jump LQG Problem for Systems with Markovian Jumping Parameters and Quadratic Cost . System and Control Letters , 10 : 349 – 356 .
  • Fragoso , MD , Costa , OLV and de Souza , CE . 1998 . A New Approach to Linearly Perturbed Riccati Equations Arising in Stochastic Control . Applied Mathematics and Optimization , 37 : 99 – 126 .
  • Ghershon , E , Shaked , U and Yaesh , I . 2005 . “ H ∞ Control and Estimation of State-MUltiplicative Linear Systems ” . In Lecture Notes in Control and Information Sciences , Vol. 318 , London : Springer-Verlag, Ltd .
  • Halanay , A and Morozan , T . 1992 . Optimal Stabilising Compensators for Linear Discrete-Time System Under Independent Random Perturbations . Revue Roumaine de Mathematiques Pures et Appliquees , 37 : 213 – 224 .
  • Ji , Y and Chizeck , HJ . 1989 . Bounded Sample Path Control of Discrete Time Jump Linear Systems . IEEE Transactions on Systems, Man, and Cybernetics , 19 : 277 – 284 .
  • Ji , Y , Chizeck , HJ , Feng , X and Loparo , K . 1991 . Stability and Control of Discrete-Time Jump Linear Systems . Control Theory and Advances Technology , 7 : 247 – 270 .
  • Mariton , M . 1990 . Jump linear systems in Automatic control , New York : Marcel Dekker .
  • Morozan , T . 1981 . Stability and Control of Some Linear Discrete-Time Systems with Jump Markov Disturbances . Revue Roumaine de Mathematiques Pures et Appliquees , 26 : 101 – 119 .
  • Morozan , T . 1983a . Optimal Stationary Control for Dynamic Systems with Markovian Perturbations . Stochastic Analysis and Applications , 1 : 299 – 325 .
  • Morozan , T . 1983b . Stabilization of Some Stochastic Discrete-Time Control Systems . Stochastic Analysis and Applications , 1 : 89 – 116 .
  • Morozan , T . 1995 . Stability and Control for Linear Discrete-Time Systems with Markov Perturbations . Revue Roumaine de Mathematiques Pures et Appliquees , 40 : 471 – 494 .
  • Morozan , T . 1996 . Dual Linear Quadratic Problem for Linear Control Systems with Jump Markov Perturbations . Revue Roumaine de Mathematiques Pures et Appliquees , 41 : 363 – 377 .
  • Rami , MA and Ghaoui , LE . 1996 . LMI Optimisation for Nonstandard Riccati Equations Arising in Stochastic Control . IEEE Transactions on Automatic Control , 41 : 1666 – 1671 .
  • Stoica , AM and Yaesh , I . 2008 . “ Kalman Type Filtering for Discrete-Time Stochastic Systems with State Dependent Noise ” . In Proceedings of the 18th International Symposium on Mathemathical Theory of Networks and Systems (MTNS 2008) , Virginia, , USA : Blacksburg (CD-Rom) .
  • Willems , JL and Willems , JC . 1976 . Feedback Stabilisation for Stochastic Systems with State and Control Dependent Noise . Automatica , 12 : 277 – 283 .
  • Wonham , WA . 1968 . On the Separation Principle of Stochastic Control . SIAM Journal on Control , 6 : 312 – 326 .

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