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...

This paper proposes a novel lifting method which converts the standard discrete-time linear periodic system to an augmented linear time-invariant system. The linear quadratic optimal control is then based on the solution of the discrete-time algebraic Riccati equation associated with the augmented linear time-invariant model. An efficient algorithm for solving the Riccati equation is derived by...

Synchronization control of coupled continuous-time linear systems is studied. For identical systems that are stabilizable, a linear feedback law obtained via algebraic Riccati equation is shown to synchronize any fixed directed network of any number of coupled systems provided that the coupling is strong enough. The strength of coupling is determined by the smallest distance of a nonzero eigenv...

First, the existence conditions on the solutions to the algebraic Riccati equation are reviewed. Then, a strict proof is presented for a necessary and sufficient condition on the existence of a unique optimal positive definite solution to this equation. By using this condition, some untrue results on the design of robust decentralized controllers are corrected.

Algebraic Riccati equations (discrete-time or continuous-time) play a fundamental role in many problems in control theory. They arise in linear-quadratic regulator problems, H ∞ or H 2-control, model reduction problems and many others. In this talk we propose numerical methods for large discrete-time algebraic Riccati equations (DARE). We present block projection methods that allow us to comput...

This paper is concerned with a stochastic linear quadratic (LQ) control problem in the infinite time horizon, with indefinite state and control weighting matrices in the cost function. It is shown that the solvability of this problem is equivalent to the existence of a so-called static stabilizing solution to a generalized algebraic Riccati equation. Moreover, another algebraic Riccati equation...

A multilayer recurrent neural network is proposed for solving continuous-time algebraic matrix Riccati equations in real time. The proposed recurrent neural network consists of four bidirectionally connected layers. Each layer consists of an array of neurons. The proposed recurrent neural network is shown to be capable of solving algebraic Riccati equations and synthesizing linear-quadratic con...