When modelling controlled dynamical systems one commonly chooses individual control variables u1, . . . um which appear natural from a physical, or practical point of view. In the case of nonlinear models evolving on R (or more generally, an analytic manifold M) that are affine in the control, such a choice corresponds to selecting vector fields f0, f1, . . . fm:M 7→ TM , and the system takes t...

In this paper we investigate the local stabilizability of single-input nonlinear affine systems by means of an estimated state feedback law given by a bilinear observer. The associated bilinear approximating system is assumed to be observable for any input and stabilizable by a homogeneous feedback law of degree zero. Furthermore, we discuss the case of planar systems which admit bad inputs (i....

In engineering practice, damping control is a usual method for stabilization. In this paper we consider nonlinear affine systems. We show that if there exists a feedback law which provides sufficiently fast convergence of trajectories (rational stabilization) then the system can also be stabilized by damping control. Our construction relies on a Liapunov function, which is basically defined as ...

A generalized non-affine nonlinear power system model is presented for a single machine bus with Static Var Compensator (SVC) or State System (SVS) hybrid Unmanned Aerial Vehicles (UAVs). The constructed by differential algebraic equations on the MATLAB-Simulink platform programming technique of its S-Function. Combining inverse method and Linear Quadratic Regulation (LQR), an optimized SVC con...

The Virasoro master equation (VME) describes the general affine-Virasoro construction T = LJaJb + iD ∂Ja in the operator algebra of the WZW model, where L ab is the inverse inertia tensor and D is the improvement vector. In this paper, we generalize this construction to find the general (one-loop) Virasoro construction in the operator algebra of the general nonlinear sigma model. The result is ...

In this paper, we consider the synthesis of Finite Time Observers for two class of nonlinear systems by solving some LMIs problem. First, we develop a method to calculate an affine gain which is used to determine an observer for a class of nonlinear systems. The method can also be applied to the case of another class of nonlinear systems with nonlinear output. A numerical example illustrates th...

This work analyzes the overall computational complexity of the stochastic Galerkin finite element method (SGFEM) for approximating the solution of parameterized elliptic partial differential equations with both affine and non-affine random coefficients. To compute the fully discrete solution, such approaches employ a Galerkin projection in both the deterministic and stochastic domains, produced...

The fundamental matrix defines a nonlinear 3D variety in the joint image space of multiple projective (or “uncalibrated perspective”) images. We show that, in the case of two images, this variety is a 4D cone whose vertex is the joint epipole (namely the 4D point obtained by stacking the two epipoles in the two images). Affine (or “para-perspective”) projection approximates this nonlinear varie...

We address the exponential synchronization problem of a leader-connected network identical nonlinear systems. suppose that each system can be made contractive by static feedback law obtained via sufficient metric-based conditions. A distributed diffusive coupling is then designed in order to solve two frameworks: case input-affine systems allowed exchange all state information its neighbour; an...