Based on symbolic manipulation program Maple and using Riccati equation mapping method several explicit exact solutions including kink, soliton-like, periodic and rational solutions are obtained for (2+1)-dimensional variable coefficient Broer-Kaup system in quite a straightforward manner. The known solutions of Riccati equation are used to construct new solutions for variable coefficient Broer...

State-dependent Riccati equation (SDRE) methods for designing control algorithms and observers for nonlinear processes entail the use of algebraic Riccati equations. These methods have yielded a number of impressive results, however, they can be computationally quite intensive and thus far they have not yielded to those attempting to assess their stability. This paper explores an alternative, t...

The majority of homing guided missiles use gimbaled seekers. The equations describing seeker gimbal system are highly nonlinear. Accurate nonlinear control of the motion of the gimbaled seeker through the attached DC motors is required. In this paper, an online technique for finite-horizon nonlinear tracking problems is presented. The idea of the proposed technique is the change of variables th...

In this paper, the projective Riccati equation method is applied to find exact solutions for fractional partial differential equations in the sense of modified RiemannLiouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the vali...

The multidelays linear control systems described by difference differential equations are often studied in modern control theory. In this paper, the delay-independent stabilization algebraic criteria and the theorem of delay-independent stabilization for linear systems with multiple time-delays are established by using the Lyapunov functional and the Riccati algebra matrix equation in the matri...

In this paper, we introduce an efficient method for solving the quadratic Riccati differential equation. In this technique, combination of Laplace transform and new homotopy perturbation methods (LTNHPM) are considered as an algorithm to the exact solution of the nonlinear Riccati equation. Unlike the previous approach for this problem, so-called NHPM, the present method, does not need the init...

Algebraic geometry plays an important role in the theory of linear systems for (at least) three reasons. First, the Laplace transform turns expressions about linear differential systems into expressions involving rational functions. In addition, many of the transformations studied in linear systems theory, like changes of coordinates or feedback, turn out to be the action of algebraic groups on...