A homeomorphic characterization of the set of solutions of a non symmetric Algebraic Riccati Equation
نویسندگان
چکیده
In this paper a very general matrix quadratic equation is considered. This equation is known in literature as asymmetric Algebraic Riccati Equation (ARE) and arises in the solution of many problems in system and control theory and applied mathematics. For this reason a large amount of work has been produced on this topic. We present a new parametrization of the set of solutions of such equation. Moreover, we prove that this parametrization is indeed given by a homeomorphic map (i.e continuous with its inverse).
منابع مشابه
Asymmetric Algebraic Riccati Equation: A homeomorphic parametrization of the set of solutions
In this paper, asymmetric Algebraic Riccati Equations are analyzed. We derive a new parametrization of the set of solutions, which may be viewed as alternative to the classical one based on Lagrangian subspaces of a “pseudo-Hamiltonian” matrix. Generalizing the symmetric case, the proposed parametrization is given in terms of pairs of invariant subspaces of two related “feedback” matrices. Exte...
متن کاملAnalytical and Verified Numerical Results Concerning Interval Continuous-time Algebraic Riccati Equations
This paper focuses on studying the interval continuous-time algebraic Riccati equation A∗X + XA + Q − XGX = 0, both from the theoretical aspects and the computational ones. In theoretical parts, we show that Shary’s results for interval linear systems can only be partially generalized to this interval Riccati matrix equation. We then derive an efficient technique for enclosing the united stable...
متن کاملLinear quadratic problems with indefinite cost for discrete time systems
This paper deals with the discrete-time infinite-horizon linear quadratic problem with indefinite cost criterion. Given a discrete-time linear system, an indefinite costfunctional and a linear subspace of the state space, we consider the problem of minimizing the costfunctional over all inputs that force the state trajectory to converge to the given subspace. We give a geometric characterizatio...
متن کاملA Solution of Riccati Nonlinear Differential Equation using Enhanced Homotopy Perturbation Method (EHPM)
Homotopy Perturbation Method is an effective method to find a solution of a nonlinear differential equation, subjected to a set of boundary condition. In this method a nonlinear and complex differential equation is transformed to series of linear and nonlinear and almost simpler differential equations. These set of equations are then solved secularly. Finally a linear combination of the solutio...
متن کاملA characterization of solutions of the discrete-time algebraic Riccati equation based on quadratic difference forms
This paper is concerned with a characterization of all symmetric solutions to the discrete-time algebraic Riccati equation (DARE). Dissipation theory and quadratic difference forms from the behavioral approach play a central role in this paper. Along the line of the continuous-time results due to Trentelman and Rapisarda [H.L. Trentelman, P. Rapisarda, Pick matrix conditions for sign-definite s...
متن کامل