Matrix spectral factorization is traditionally described as finding spectral factors having a fixed analytic pole configuration. The classification of spectral factors then involves studying the solutions of a certain algebraic Riccati equation which parametrizes their zero structure. The pole structure of the spectral factors can be also parametrized in terms of solutions of another Riccati eq...

In this paper null controllability with vanishing energy for discrete-time systems is considered. As in the case of continuous time systems necessary and sufficient conditions in terms of an algebraic Riccati equation are given. Then necessary and sufficient conditions involving the eigenvalues of the state matrix are given. Reachability and controllability with vanishing energy are also consid...

The first part of the paper concerns the existence of strongly stabilizing solutions to the standard algebraic Riccati equation for a class of infinite-dimensional systems of the form Z(A,B,S V2B*,D), where A is dissipative and all the other operators are bounded. These systems are not exponentially stabilizable and so the standard theory is not applicable. The second part uses the Riccati equa...

In this paper, a missile longitudinal autopilot is designed using a new nonlinear control synthesis technique (called theθ -D approximation). The particular D θ − methodology used in this paper is referred to as the D θ − 2 H design. The D θ − technique can achieve suboptimal solutions to a class of nonlinear optimal control problems in the sense that it solves the Hamilton-Jacobi-Bellman (HJB)...

In this paper we show how to exactly decompose the algebraic Riccati equations of deterministic multimodeling in terms of one pure-slow and two pure-fast algebraic Riccati equations. The algebraic Riccati equations obtained are of reduced-order and nonsymmetric. However, their ( ) perturbations (where = and , are small positive singular perturbation parameters) are symmetric. The Newton method ...

When Newton’s method is applied to find the maximal symmetric solution of an algebraic Riccati equation, convergence can be guaranteed under moderate conditions. In particular, the initial guess need not be close to the solution. The convergence is quadratic if the Fréchet derivative is invertible at the solution. In this paper we examine the behaviour of the Newton iteration when the derivativ...

An iterative algorithm to solve a kind of state-perturbed stochastic algebraic Riccati equation (SARE) in LQ zero-sum game problems is proposed. In our algorithm, we replace the problem of solving a SAREwith an indefinite quadratic term by the problem of solving a sequence of SAREs with a negative semidefinite quadratic term, which can be solved by existing methods. Under some appropriate condi...

In this note we present equations that uniquely determine the maximumpossible imaginaryvalue of the closed loop eigenvalues in an LQ-optimal system, irrespective of how the state weight matrix is chosen, provided a real symmetric solution of the algebraic Riccati equation exists. In addition, the corresponding state weight matrix and the solution to the algebraic Riccati equation are derived fo...

The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furtherm...