A stabilization theorem for Fell bundles over groupoids

We study the C*-algebras associated with upper semi-continuous Fell bundles over second-countable Hausdorff groupoids. Based on ideas going back to the Packer–Raeburn ‘stabilization trick’, we construct from each such bundle a groupoid dynamical system whose associated Fell bundle is equivalent to the original bundle. The upshot is that the full and reduced C*-algebras of any saturated upper semi-continuous Fell bundle are stably isomorphic to the full and reduced crossed products of an associated dynamical system. We apply our results to describe the lattice of ideals of the C*-algebra of a continuous Fell bundle by applying Renault's results about the ideals of the C*-algebras of groupoid crossed products. In particular, we discuss simplicity of the Fell-bundle C*-algebra of a bundle over G in terms of an action, described by Ionescu and Williams, of G on the primitive-ideal space of the C*-algebra of the part of the bundle sitting over the unit space. We finish with some applications to twisted k-graph algebras, where the components of our results become more concrete.

ADAPTIVE SLIDING-MODE CONTROL: SIMPLEX-TYPE METHOD

The simplex method is easy and brief for designing the sliding mode, but it also has some disadvantages. Since the control vectors are constant, the chattering phenomenon also occurs when switching control takes place in simplex-type SMC scheme. Hence, we make few modifications to the simplex method that form an irregular simplex such that it improves the choice of simplex control vector and chattering phenomenon. The irregular simplex is obtained by an adaptive control law. The stabilization of a nonlinear multi-input system by using adaptive control based on simplex-type sliding-mode control philosophy is examined in this paper. The adaptive law and stabilization theorem are proposed and proved. The simulation results demonstrate that the simplex-type adaptive sliding-mode control proposed in this paper is a good solution to the chattering problem in the simplex sliding-mode control.

SIMPLE LMI-BASED SYNCHRONIZATION OF FRACTIONAL-ORDER CHAOTIC SYSTEMS

This paper presents a simple scheme for synchronization of fractional-order chaotic systems. The scheme utilizes a recently developed LMI (Linear matrix inequality) stabilization theorem for fractional-order linear interval systems to design a linear controller. In contrast to existing schemes in the literature, the present scheme is straightforward and does not require that nonlinear parts of synchronization error dynamics are cancelled by the controller. The fractional-order Rössler, Lorenz, and hyperchaotic Chen systems are used as demonstrative examples. Numerical results illustrate the effectiveness of the present scheme.

Delay Independent Control of Bilateral Teleoperation Based on LMI

This paper presents a delay independent algorithm for bilateral control system which necessary uses for achieving in teleoperation. The system uses a state space expression to implement error dynamic equation with a tow channel structure. Then, several linearity matrix inequations (LMI) called stabilization theorem are constructed. Lyaponov function method is used to prove the stabilization theorem. Experimental results show that our approach is valid and has encouraging stabilization performance.