Hermitian solutions of the discrete-time algebraic Riccati equation

REFERENCES

• BITTANTI , S. , BOLZERN , P. , and COLANERI , P. , 1986 , Inertia theorems for Lyapunov and Riccati equations an updated view . Proceedings SIAM Conference on Linear Algebra in Signals , Systems and Control , Boston , Massachusetts , pp. 11 – 35 .
   Google Scholar
• DE SOUZA , C. E. , GEVERS , M R. , and GOODWIN , G. C. , 1986 , Riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices . IEEE Transactions on Automatic Control , 31 , 831 – 838 .
   Web of Science ®Google Scholar
• DELCHAMPS , D. F. , 1980 , A note on the analiticity of the Riccati metric . Algebraic and Geometric Methods in Linear Systems Theory . Lecture Notes in Applied Mathematics , Vol. 18 , edited by C. I. Byrns and C.F.Martin ( American Mathematics Society , Providence , Rhode Island , U.S.A. 37 – 41 ; 1984, Analytic feedback control and the algebraic Riccati equation. IEEE Transactions on Automatic Control, 29, 1031–1033.
   Google Scholar
• FAIBUSOVICH , L. E. , 1986 , Algebraic Riccati equation and symplectic algebra . International Journal of Control , 39 , 781 – 791 .
   Google Scholar
• GOHBERG , I. , LANCASTER , P. , and RODMAN , L. , 1986 , Invariant Subspaces of Matrices ( New York Wiley ).
   Google Scholar
• IONESCU , V. , and WEISS , M. , 1992 , On computing the stabilizing solution of the discrete-time Riccati equation . Linear Algebra Applications , 174 , 229 – 238 .
   Web of Science ®Google Scholar
• KUčERA , V. , 1991 , Algebraic Riccati equations Hermitian and definite solutions . The Riccati Equation , edited by S. Bittanti et al. ( Berlin Springer-Verlag ), pp. 53 – 88 .
   Google Scholar
• LANCASTER , P. , RAN , A. C. M. , and RODMAN , L. , 1986 , Hermitian solutions of the discrete algebraic Riccati equation . International Journal of Control , 44 , 777 – 802 .
   Web of Science ®Google Scholar
• LAUB , A. J. , 1991 , Invariant subspace methods for the numerical solution of Riccati equations . The Riccati Equation , edited by S. Bittanti et al. ( Berlin Springer-Verlag ), pp. 163 – 196 .
   Google Scholar
• MEHRMANN , V. , 1989 , Linear algebra problems in linear quadratic optimal control . Linear Algebra Applications , 121 , 291 – 331 .
   Google Scholar
• MOLINARI , B. P. , 1975 , The stabilizing solution of the discrete algebraic Riccati equation . IEEE Transactions on Automatic Control , 20 , 396 – 399 .
   Web of Science ®Google Scholar
• PAPPAS , T. , LAUB , A. , and SANDELL , N. JR. , 1980 , On the numerical solution of the discrete-time algebraic Riccati equations . IEEE Transactions on Automatic Control , 25 , 631 – 641 .
   Web of Science ®Google Scholar
• RAN , A. C. M. , and RODMAN , L. , 1984 , The algebraic matrix Riccati equation . Operator Theory: Advances and Applications , Vol. 12 ( Basel , Switzerland Birkhauser ), pp. 351 – 381 .
   Google Scholar
• RAN , A. C. M. , and TRENTELMAN , H. L. , 1993 , Linear quadratic problems with indefinite cost for discrete time systems . SIAM Journal on Matrix Analysis and Applications , 14 , 776 – 797 .
   Google Scholar
• SCHERER , C. , 1991 , The solution set of the algebraic Riccati equation and the algebraic Riccati inequality . Linear Algebra Applications , 153 , 99 – 122 .
   Web of Science ®Google Scholar
• WIMMER , H. K. , 1991 , Normal forms of symplectic pencils and the discrete-time algebraic Riccati equation . Linear Algebra Application , 147 , 411 – 440 ; 1992, Unmixed solutions of the discrete-time algebraic Riccati equation. SIAM Journal of Control Optimization, 30, 867–878; 1995, Isolated solutions of the continuous-time algebraic Riccati equation. Integral Equations Operator Theory, 21, 362–375.
   Web of Science ®Google Scholar