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Dealing with impulsive effects is one of the most challenging problems in the field of fixed-time control. In this paper, we solve this challenging problem by considering fixed-time synchronization of complex networks (CNs) with impulsive effects. By designing a new Lyapunov function and constructing comparison systems, a sufficient condition formulated by matrix inequalities is given to ensure that all the dynamical subsystems in the CNs are synchronized with an isolated system in a settling time, which is independent of the initial values of both the CNs and the isolated system. Then, by partitioning impulse interval and using the convex combination technique, sufficient conditions in terms of linear matrix inequalities are provided. Our synchronization criteria unify synchronizing and desynchronizing impulses. Compared with the existing controllers for fixed-time and finite-time techniques, the designed controller is continuous and does not include any sign function, and hence, the chattering phenomenon in most of the existing results is overcome. An optimal algorithm is proposed for the estimation of the settling time. Numerical examples are given to show the effectiveness of our new results. [ABSTRACT FROM AUTHOR]

In this article, a methodology of chattering analysis of Sliding Mode/Higher Order Sliding Mode (SM/HOSM) control systems in the frequency domain is presented. A numerical method for computing the Describing Functions (DFs) of HOSM control algorithms is given. The algorithm for predicted chattering parameters in dynamically perturbed system via the Describing Function-Harmonic Balance (DF-HB) technique is proposed. The stability conditions for limit cycles in dynamically perturbed HOSM control systems are presented. The concepts of Practical Stability Phase Margin ( PSPM) and Practical Stability Gain Margin (PSGM) as the robustness metrics to unmodeled dynamics in HOSM control systems are introduced. The methodologies for computing PSPM and PSGM via DF-HB technique are provided. The accuracy of the proposed chattering analysis techniques is confirmed via computer simulations. [ABSTRACT FROM AUTHOR]

This technical note discusses to what extent the high order sliding mode control may serve as an alternative to the conventional sliding mode control. Definition of sliding mode order, relative degree, chattering attenuation, filtering, and implementation complexity constitute the scope of the discussion. [ABSTRACT FROM PUBLISHER]

In this paper the multi-input Sliding Mode control of nonlinear uncertain non-affine systems with mono-directional actuators is considered. The geometric properties of the regular simplices of vectors are exploited by the mono-directional actuation system. The proposed full-state feedback control method introduces integrators in the input channel and suitably modifies the sliding output to be steered to zero. The resulting high frequency gain matrix (HFGM), which is the matrix multiplying the control vector, turns out to be affected by time and state dependent uncertainties. An effective use of the integral Sliding Mode method in connection with a non-conventional simplex based switching logic is introduced. The proposed simplex control procedure is adequately designed to avoid any possible unbounded increment of the control actions despite the presence of integrators in the input channel and the exploitation of mono-directional devices. [ABSTRACT FROM AUTHOR]

A formal mathematical definition of chattering is proposed. Chattering phenomena are classified into three types. In particular, the first type is harmless and cannot be avoided. Chattering properties of various control approaches are considered. The dangerous second and third types of chattering phenomena are proved to be removable by proper use of high-order sliding-modes (HOSM). Fast stable actuators and sensors only generate the first type of chattering in HOSM systems and practically never affect the sliding motion. Computer simulation confirms the theoretical results. [ABSTRACT FROM AUTHOR]

It is shown that the higher the order r of the homogeneous sliding mode is, the less sensitive it is to the presence of unaccounted-for fast stable actuators. With μ being an infinitesimal actuator time constant, the sliding variable magnitude is proved to be proportional to μr. The system chattering is shown to be not amplified in the presence of actuators. [ABSTRACT FROM AUTHOR]

For a sliding mode (SM) system containing parasitic dynamics, a model of chattering and a model of the averaged motions of the order equal to the original order of the system are obtained via the use of the locus of a perturbed relay system (LPRS) method. The latter model proves that the averaged motions in an SM system differ from those in the reduced-order model. In particular, such phenomena as the nonideal disturbance rejection and the nonideal input tracking are observed. It is shown that the non-reduced-order model transforms into the reduced one when the parasitic dynamics are removed. Yet, the chattering and the averaged motion—being the two components of the motion in the SM system—belong to two different frequency ranges (spectra). As a result, a frequency characteristic shaping aimed at achieving the desired frequency of chattering and enhancing the closed-loop performance becomes possible. This opportunity is explored in this paper. Examples that illustrate the proposed approach are provided. [ABSTRACT FROM AUTHOR]

For sliding-mode control systems with fast actuators, sufficient conditions for the exponential decreasing of the amplitude of chattering and unlimited growth of frequency are found. The connection between the stability of actuators and the stability of the plant on the one hand and the stability of the sliding-mode system as the whole on the other hand is investigated. The algorithm for correction of sliding-mode equations is suggested for taking into account the presence of fast actuators. [ABSTRACT FROM AUTHOR]

Analyzes the singularly perturbed relay control systems (SPRCS) models of chattering in the small neighborhood of the switching surface in sliding mode systems. Existence and stability of fast periodic solutions to SPRCS; Analysis of averaged equations in sliding mode with fast actuators.

Presents the exact solution to the minimum-time optimal control problem of a single-degree-of-freedom (DOF) mechanical system with friction by extending Pontryagin's maximum principle to the case of nonsmooth vector fields and transversality condition. Demonstration of practical use using a single-DOF robotic manipulator; Prevention of chattering phenomena.

Presents a solution to the problem of eliminating the chaterring effect. Reliance of the solution procedure on the application of an original control approach; Application of the approach to single-input nonlinear systems with particular type of uncertainties; Extension of the result to multi-input nonlinear systems.

Focuses on the existence of solutions to a class of nonlinear convergent chattering-free sliding mode control systems. Ways to counter the chattering phenomenon; Control laws producing chattering-free sliding mode.

Presents the contribution to the solution to the chattering elimination problem associated with variable structure control. Details on such a solution; Information on the proposed algorithm.

Presents a paper on the chattering reduction and error convergence in the sliding-mode control of a class of nonlinear systems. How to reduce chattering in sliding-mode control; Information on sliding-mode control.

An unfortunate mistake in the proof of Proposition 1 in the above paper is corrected. [ABSTRACT FROM PUBLISHER]