In this paper we show how some difficult linear algebra problems can be “approximately” solved using statistical learning methods. We illustrate our results by considering the state and output feedback, finite-time robust stabilization problems for linear systems subject to time-varying norm-bounded uncertainties and to unknown disturbances. In the state feedback case, we have obtained in an ea...

This work investigates the finite-time stability (FTS) issue for a class of inertial neural networks (INNs) with mixed-state time-varying delays, proposing novel analytical approach. Firstly, we establish FTS lemma, which is entirely different from existing theorems, and extend current research results. Secondly, an improved discontinuous reliable control mechanism developed, more valid widens ...

with the growing population and density in metropolitan areas, higher tendency to live in high-rise buildings, and increasing demand for parking lots, it seems necessary to excavate soil to construct underground spaces. during excavation work, as the height of the wall increases, special care should be taken to the wall stabilization to avoid any consequent damage including extensive property d...

This paper presents a continuous composite control scheme to achieve fixed-time stabilization for nonlinear systems with mismatched disturbances. The composite controller is constructed in two steps: First, uniformly finite time exact disturbance observers are proposed to estimate and compensate the disturbances. Then, based on adding a power integrator technique and fixed-time stability theory...

We present a method of combining a self-stabilizing algorithm with a hierarchical structure to construct a self-stabilizing algorithm with improved stabilization time complexity and fault-containment features. As a case study, a self-stabilizing spanning-tree algorithm is presented which in favorable settings has logarithmic stabilization time complexity.

This paper investigates a quaternion-based finite time attitude synchronization and stabilization problem for satellite formation flying. Sufficient conditions are presented for finite time boundness and stability of this distributed consensus problem. More specifically, a nonlinear control law based on a finite time control technique is developed such that the attitude of the rigid spacecraft ...

The finite-time stabilization problem for a class of networked control systems with state delay is considered in this paper. With Lyapunov theorem, a sufficient condition for the design of a state feedback controller which makes the closed loop system finite-time stable is provided. And, the sufficient condition is given in terms of linear matrix inequality. A numerical example is presented to ...

Establishing and exactly keeping constraints of high relative degrees is a central problem of the modern sliding-mode control. Its solution in finite-time is based on so-called high-order sliding modes, and is reduced to finite-time stabilization of an auxiliary uncertain system. Such stabilization is mostly based on the homogeneity approach. Robust exact differentiators are also developed in t...

A new nonlinear design technique for finite time stabilization of a class of nonlinear systems is developed using backstepping method. This method is able to apply strict feedback form systems. An example illustrates the theoretical results.

Abstract: This paper investigates the problem of global finite-time stabilization by state feedback for a class of stochastic nonlinear systems with low-order nonlinearities, to which the existing control methods are inapplicable. By skillfully adopting the method of adding a power integrator and constructing twice continuous differential Lyapunov functions, a stepwise constructive continuous s...