This paper presents a study of linear control systems based on exact feedback linearization and approximate feedback linearization. As exact feedback linearization is applied, a linear controller can perform the control objectives. The approximate feedback linearization is required when a nonlinear system presents a noninvolutive property. It uses a Taylor series expansion in order to compute a...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii CHAPTER 1. INTRODUCTIOIN . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Robust Feedback Linearization . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Application to Hydraulic System . . . . . . . . . . . . . . . . . . . . . . 5...

The singularity manifold equation of the Kadomtsev-Petviashvili equation, the so-called Krichever-Novikov equation, has an exact linearization to an overdetermined system of partial diierential equations in three independent variables. We study in detail the Cauchy problem for this system as an example for the use of the formal theory of diierential equations. A general existence and uniqueness...

This paper proposes two methods for nonlinear observer design which are based on a partial nonlinear observer canonical form (POCF). Observability and integrability existence conditions for the new POCF are weaker than the well-established nonlinear observer canonical form (OCF), which achieves exact error linearization. The proposed observers provide the global asymptotic stability of error dy...

This paper employs the computational iterative approach known as Spectral Local Linearization Method (SLLM) to analyze Hall effect on MHD flow and heat transfer over an unsteady stretching permeable surface in the presence of thermal radiation and heat source/sink. To demonstrate the reliability of our proposed method, we made comparison with Matlab bvp4c routine technique and excellent agreeme...

In this paper we develop a robust controller based on variable structure systems (VSS) control theory for the stabilization of a class of Underactuated Mechanical Systems. This controller is based on a noncollocated partial feedback linearization of the underactuated system with a particular choice of the additional control for which the design is made using the sliding mode approach. Simulatio...

This paper tackles the combined problem of trajectory planning and tracking control of planar underactuated marine vehicles with different dynamic models. A reference feasible trajectory for the position and orientation is planned so as to be consistent with each of the three dynamic models. Using these reference values the dynamics of the vehicles is transformed to the error one. Partial state...

We introduce a new notion of linear stability for standing waves of the nonlinear Schrödinger equation (NLS) which requires not only that the spectrum of the linearization be real, but also that the generalized kernel be not degenerate and that the signature of all the positive eigenvalues be positive. We prove that excited states of the NLS are not linearly stable in this more restrictive sens...

Existing work for abstractive multidocument summarization utilise existing phrase structures directly extracted from input documents to generate summary sentences. These methods can suffer from lack of consistence and coherence in merging phrases. We introduce a novel approach for abstractive multidocument summarization through partial dependency tree extraction, recombination and linearization...

We apply a relatively new technique which is called the homotopy perturbation method (HPM) for solving linear and nonlinear partial differential equations. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are ...