We consider the nonsymmetric algebraic Riccati equation for which the four coefficient matrices form an M -matrix. Nonsymmetric algebraic Riccati equations of this type appear in applied probability and transport theory. The minimal nonnegative solution of these equations can be found by Newton’s method and basic fixed-point iterations. The study of these equations is also closely related to th...

By means of Riccati transformation techniques, we establish some oscillation criteria for a second order nonlinear dynamic equation on time scales in terms of the coefficients. We give examples of dynamic equations to which previously known oscillation criteria are not applicable.

This paper deals with two interrelated issues. One is an invariant subspace approach to finding solutions for the algebraic Riccati equation for a class of infinite dimensional systems. The second is approximation of the solution of the algebraic Riccati equation by finite dimensional approximants. The theory of exponentially dichotomous operators and bisemigroups is instrumental in our approach.

A class of second-order nonlinear differential equations with a damping term is investigated in this paper. By using the Riccati transformation technique and general weight functions, we obtain some new sufficient conditions for the oscillation of the equation. Our results improve and extend some known results. Two examples are given to illustrate the main results.

By means of generalized Riccati transformation techniques and generalized exponential functions, we give some oscillation criteria for the nonlinear dynamic equation (p(t)x ∆ (t)) ∆ + q(t)(f • x σ) = 0, on time scales. We also apply our results to linear and nonlinear dynamic equations with damping and obtain some sufficient conditions for oscillation of all solutions.

We consider a splitting-based approximation of the abstract Riccati equation in the setting of Hilbert–Schmidt operators. The Riccati equation arises in many different areas and is important within the field of optimal control. While convergence of different methods for approximating the Riccati equation is discussed in several studies, none of them rigorously prove an order of convergence. In ...

In this paper, we study an eigenvalue problem for stochastic Hamiltonian systems driven by a Brownian motion and Poisson process with boundary conditions. By means of dual transformation and generalized Riccati equation systems, we prove the existence of eigenvalues and construct the corresponding eigenfunctions. Moreover, a specific numerical example is considered to illustrate the phenomenon ...

A solution X of a discrete-time algebraic Riccati equation is called unmixed if the corresponding closed-loop matrix Φ(X) has the property that the common roots of det (sI−Φ(X)) and det (I− sΦ(X)∗) (if any) are on the unit circle. A necessary and sufficient condition is given for existence and uniqueness of an unmixed solution such that the eigenvalues of Φ(X) lie in a prescribed subset of C. A...

This paper develops an anti-windup scheme for systems with rate-limited actuators. The main results show how a full-order anti-windup compensator can be synthesised using an algebraic Riccati equation and several free parameters. A further result then shows how the free parameters may be chosen to influence, in an intuitive way, the local L2 gain of the system and the size of the region of attr...

This paper considers the optimal control problem for the bilinear system based on state feedback. Based on the concept of relative order of the output with respect to the input, first we change a bilinear system to a pseudo linear system model through the coordinate transformation. Then based on the theory of linear quadratic optimal control, the optimal controller is designed by solving the Ri...