In this paper, we extend the sliding mode idea to a class of unmatched uncertain variable structure systems. This method is achieved with introducing a new terminal sliding variable and the finite time stability of proposed method is proved using a new particular finite time condition in both reaching and sliding phases. In reaching phase a new sliding mode controller is derived to guarantee th...

This paper describes a set of delay-dependent IQC stability conditions for time-delay uncertainty. The IQC’s are linearly parameterized in terms of a pair of rational stability multipliers, each active over one of a pair of complementary frequency intervals. Using the finite-frequency positive real lemma, each of these finite-frequency IQC conditions are shown to be equivalent to a frequency-in...

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 ...

In this paper, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control design for finite-time partial stability and finite-time, partial-state stabilization. Finite-time partial stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system st...

In this paper, a new smooth second order sliding mode control is proposed. This algorithm is a modified form of Super Twisting algorithm. The Super Twisting guarantees the asymptotic stability, but the finite time stability of proposed method is proved with introducing a new particular Lyapunov function. The Proposed algorithm which is able to control nonlinear systems with matched structured u...

This paper presents the double chain–integrator finite-time convergence in a closed loop with second-order bang–bang sliding control. The direct Lyapunov method carried out stability analysis and reaching time estimation using suitable non-smooth strong function. That is, proposed energy function is strictly positive definite, definite negative derivative. Additionally, estimates presence of ma...

We use the ideas of Adly, Attouch, and Cabot [in Nonsmooth Mechanics Analysis, Adv. Mech. Math. 12, Springer, New York, 2006, pp. 289--304] on finite-time stabilization dry friction oscillators to establish a theorem differential inclusions with moving polyhedral constraint (known as sweeping processes) form $C+c(t)$. then employ Moreau Variational Techniques in Mathematical Physics (Centro Int...

Abstract. In this paper, a high-order nonlinear integral-derivative observer is presented based on finitetime stability and singular perturbation technique. The proposed integral-derivative observer can not only obtain the multiple integrals of a signal, but can also estimate the derivatives. Conditions are given ensuring finite-time stability for the presented integral-derivative observer, and...