On necessary and sufficient conditions for output finite-time stability

International audienceOutput global finite-time stability of locally Lipschitz continuous autonomous systems is characterized by means of smooth Lyapunov functions. The so-called output-Lagrange stable systems are studied with details. Influence of a kind of continuity of the settling-time function is considered. Necessary and sufficient conditions of output finite-time stability are presented. The theoretical results are supported by academic examples and numerical simulations

On finite-time stability analysis of homogeneous Persidskii systems using LMIs

International audienceThe paper provides a sufficient condition to ensure robust finite-time stability of homogeneous generalized Persidskii systems. The proposed condition is formulated using linear matrix inequalities and it allows to obtain settling time estimates. The results are supported with numerical examples

Homogeneity Based Finite/Fixed-Time Observers for Linear MIMO Systems

International audienceThe paper is devoted to the problem of finite-time and fixed-time observation of linear multiple input multiple output control systems. The proposed dynamic observers do not require system transformation to a canonical form and guarantee convergence of the observation error to zero in a finite or in a fixed time. It is shown that the observers are robust (in input-to-state sense) against input disturbances and measurement noises. The results are supported with simulation examples

On Notions of Output Finite-Time Stability

International audienceLyapunov characterizations of output finite-time stability are presented for the system $x' = f (x), y = h(x)$ which is locally Lipschitz continuous out of the set $Y = {x ∈ R n : h(x) = 0}$ and continuous on $R^n$. The definitions are given in the form of $K$ and $KL$ functions. Necessary and sufficient conditions for output finite-time stability are given using Lyapunov functions. The theoretical results are supported by numerical examples

Independent of delay stabilization using implicit Lyapunov function method

International audienceNonlinear implicit Lyapunov function based control algorithms with delay in control and/or measurement channel are presented. The proposed control algorithms provide global asymptotic stability for all delays less than a certain threshold value and global asymptotic stability with respect to a compact set containing the origin for any delay over the threshold value. The algorithms are also applicable for the fast-varying delay and sampled-data cases. The theoretical results are supported by numerical simulations and comparison

Control of Systems with Arbitrary Bounded Input Delay Using Implicit Lyapunov Function Technique

International audienceThe paper presents control algorithms for systems with input delay. There are two main results based on using Implicit Lyapunov Function (ILF) technique: 1) an LMI-based approach is presented to evaluate the domain of attraction of a finite-time stable control in the case of the arbitrary bounded delayed control input; 2) a uniting control is designed with commutation between two laws providing a global boundedness of all trajectories of systems with any input delay, and convergence to the origin for a sufficiently small one. The results are also preserved for the time-varying delay case. The theoretical results are supported by numerical examples

Homogeneous Observer Design for Linear MIMO Systems

International audienceThe paper is devoted to the problem of state observation (particularly, in finite time) of linear MIMO systems. The presented nonlinear observer does not require system transformation to a canonical form and guarantees finite-time (asymptotic with a fixed-time attraction of any compact set containing the origin) stability of observation error equation if homogeneity degree is negative (positive). The proposed observer is robust in input-to-state sense with respect to disturbances and measurement noises. Performance of the observer is illustrated by a numerical example

A brief analysis of the use of non-linear time-frequency filtering for processing ECG signals

Some current trends of the use of non-linear time-frequency filtering approach to ECG signal processing are discussed herein. A brief review of an application potentiality of non-linear filtration is offered for long-term ECG signal processing. Possible problems of long-term monitoring, related to measurements interference and noise of ECG signal, are revealed. To eliminate the revealed problems, in further research, an implementation of a processing system using the non-linear-threshold time-frequency filtering method is planned. It is expected to improve an accuracy of cardiac data processing considering features of interference and measurement noise of different intensity

Transition of the Russian federation to new educational standard: independent work of students as a factor in the quality of educational process*

The paper is devoted to changes in the organization of independent work of students. These changes are associated with transition of the Russian Federation to new educational standards. In this regard, systemically-active approach to educational process, which is also called competence-based approach, comes to replace the knowledge-based model of education. Independent work of students as one of the main components of the competence-based approach is aimed not only at achieving of educational goals, but mainly on the formation of personal qualities of the future specialist - self-knowledge, self-development and self-realization. These qualities form a new competent person who meets the requirements of the labor market. The research includes consideration of issues such as organization, planning, monitoring methods of self-dependent student work taking into account the requirements of the educational standard

Frequency Domain Analysis of Control System Based on Implicit Lyapunov Function*

International audience— A frequency domain analysis of implicit Lyapunov function-based control system [14] is developed for the case of finite-time stabilizing feedback law. The Gang of Four and loop transfer function are considered for practical implementation of the control via frequency domain control design. The effectiveness of this control scheme is demonstrated on an illustrative example of roll control for a vectored thrust aircraft