We consider multi-grid, or more appropriately, multi-level techniques for the numerical solution of operator Lyapunov and algebraic Riccati equations. The Riccati equation, which is quadratic, plays an essential role in the solution of linear-quadratic optimal control problems. The linear Lyapunov equation is important in the stability theory for linear systems and its solution is the primary s...

In this paper, we study the existence of linear quadratic Gaussian (LQG)–balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show that the control (filter) Riccati equation has a nonnegative self-adjoint solution if and only if...

We consider multi-grid, or more appropriately, multi-level techniques for the numerical solution of operator Lyapunov and algebraic Riccati equations. The Riccati equation, which is quadratic, plays an essential role in the solution of linear-quadratic optimal control problems. The linear Lyapunov equation is important in the stability theory for linear systems and its solution is the primary s...

where D−y is the Liouville right-sided fractional derivative of order a Î (0,1) of y and h >0 is a quotient of odd positive integers. We establish some oscillation criteria for the equation by using a generalized Riccati transformation technique and an inequality. Examples are shown to illustrate our main results. To the best of author’s knowledge, nothing is known regarding the oscillatory beh...

This paper presents a simple and efficient method for determining the solution of Riccati differential equation with coefficients rational. In case the differential Galois group of the differential equation (E l) : y = ry, r ∈ C(x) is reducible, we look for the rational solutions of Riccati differential equation θ + θ 2 = r, by reducing the number of check to be made and by accelerating the sea...

in this paper, the dierential transform method (dtm) is applied to the fisherequation. this method can be used to obtain the exact solutions of fisherequation. finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial dierential equations. these resultsshow that this technique is easy to apply.

In this paper, we study the linear quadratic Nash games for infinite horizon singularly perturbed systems. In order to solve the problem, we must solve a pair of cross–coupled algebraic Riccati equations with a small positive parameter ε. As a matter of fact, we propose a new algorithm, which combines Lyapunov iterations and the generalized Lyapunov equation direct method, to solve the cross–co...

In this paper based on a system of Riccati equations with variable coefficients, we presented a new Riccati equation with variable coefficients expansion method and its algorithm, which are direct and more powerful than the tanh-function method, sine-cosine method, the generalized hyperbolic-function method and the generalized Riccat equation with constant coefficient expansion method to constr...