Related papers: Unconditionnally stable scheme for Riccati equatio…
In this paper we present a numerical scheme for the resolution of matrix Riccati equation, usualy used in control problems. The scheme is unconditionnaly stable and the solution is definite positive at each time step of the resolution. We…
In this paper, we provide the following simple equivalent condition for a nonsymmetric Algebraic Riccati Equation to admit a stabilizing cone-preserving solution: an associated coefficient matrix must be stable. The result holds under the…
Simultaneous stabilization problem arises in various systems and control applications. This paper introduces a new approach to addressing this problem in the multivariable scenario, building upon our previous findings in the scalar case.…
Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and $H^\infty$ control theory. In this work, we study the properties of one type of discrete-time algebraic Riccati…
We are concerned with efficient numerical methods for stochastic continuous-time algebraic Riccati equations (SCARE). Such equations frequently arise from the state-dependent Riccati equation approach which is perhaps the only systematic…
This paper addresses an open problem in the area of linear quadratic optimal control. We consider the regular, infinite-horizon, stability-modulo-a-subspace, indefinite linear quadratic problem under the assumption that the dynamics are…
The control algebraic Riccati equation is studied for a class of systems with unbounded control and observation operators. Using a dichotomy property of the associated Hamiltonian operator matrix, two invariant graph subspaces are…
This note concerns a class of matrix Riccati equations associated with stochastic linear-quadratic optimal control problems with indefinite state and control weighting costs. A novel sufficient condition of solvability of such equations is…
Algebraic Riccati equations with indefinite quadratic terms play an important role in applications related to robust controller design. While there are many established approaches to solve these in case of small-scale dense coefficients,…
A stable approach for integrating the impedance matrix in cylindrical, radial inhomogeneous structures is developed and studied. A Stroh-like system using the time-harmonic displacement-traction state vector is used to derive the Riccati…
We study the time-inconsistent linear quadratic optimal control problem for forward-backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research…
An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. We introduce a new approach to solve a class of…
Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in various control theory applications. This work demonstrates that when the matrix coefficients of the equation are quasiseparable, the solution…
We consider matrix Riccati inequality arising in the theory of absolute stability, $H_\infty$ control problem, $LQ$ problem, and optimal estimation problem. In the case of sign definite frequency domain function, the solvability of Riccati…
We use a new approach with a matrix transformation to obtain a new global solvability criterion for matrix Riccati equations. The proven theorem completes an well known result in directions of extension of classes of coefficient of…
This paper proposes a novel iterative algorithm to compute the stabilizing solution of regime-switching stochastic game-theoretic Riccati differential equations with periodic coefficients. The method decomposes the original complex…
A linear quadratic optimal stochastic control problem with random coefficients and indefinite state/control weight costs is usually linked to an indefinite stochastic Riccati equation (SRE) which is a matrix-valued quadratic backward…
Direct solution of simultaneous linear equations is regarded to be slow for large systems of equations and requires special treatment to avoid numerical instability. A new method is proposed that addresses the numerical instability without…
Many important initial value problems have the property that energy is non-increasing in time. Energy stable methods, also referred to as strongly stable methods, guarantee the same property discretely. We investigate requirements for…
An oblique projections based feedback stabilizability result in the literature is extended to a larger class of reaction-convection terms. A discussion is presented including a comparison between explicit oblique projections base feedback…