Introduction  About Riccati and his equation   Non-symmetric Algebraic Riccati Equation (NARE)       Continuous time ARE (CARE) Numerical methods for solving ARE
                                   Algebraic Riccati Equation
                                                        Bibhas Adhikari
                                                    IIT Kharagpur, India
                          GIANcourseonSingular Optimal Control, 2016
    Introduction  About Riccati and his equation   Non-symmetric Algebraic Riccati Equation (NARE)       Continuous time ARE (CARE) Numerical methods for solving ARE
    Outline
            1     Introduction
                      TheModelandtheProblem
                      References
            2     AboutRiccati and his equation
            3     Non-symmetricAlgebraic Riccati Equation (NARE)
                      Critical solutions
            4     Continuous time ARE (CARE)
                      Critical solutions
            5     Numerical methods for solving ARE
    Introduction  About Riccati and his equation   Non-symmetric Algebraic Riccati Equation (NARE)       Continuous time ARE (CARE) Numerical methods for solving ARE
    References
               1    Dario A. Bini, Bruno Iannazzo and Beatrice Meini,
                    Numerical Solution of Algebraic Riccati Equations, SIAM,
                    2012.
               2    Sergio Bittanti, Alan J. Laub and Jan C.Willems (Eds.) The
                    Riccati Equation, Springer, 1991.
               3    Peter Lancaster and Leiba Rodman, Algebraic Riccati
                    Equations, Oxford University Press, 1995.
               4    JamesF.Bellon, Riccati Equations in Optimal Control
                    Theory, Masters Thesis, Georgia State University, 2008.
               5    W.T. Reid, Riccati Differential Equations, in volume 86 of
                    Mathematics in Science and Engineering, Academic
                    Press, New York, 1972.
               6    Israel Gohberg, Peter Lancaster and Leiba Rodman,
                    Invariant Subspaces of Matrices with Applications, SIAM,
                    2006.
    Introduction  About Riccati and his equation   Non-symmetric Algebraic Riccati Equation (NARE)       Continuous time ARE (CARE) Numerical methods for solving ARE
    AboutRiccati and his equation
                                              C+XA+DX−XBX=0
           Special case: A,B,C,D are real/complex numbers!!