STABILITY OF DISCONTINUOUS NONLINEAR SINGULAR SYSTEMS

This paper studies a class of nonlinear singular systems with discontinuous right-hand sides,it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle.In this paper,LaSalle invariance principle of the discontinuous nonlinear singular systems is presented firstly.Furthermore,some sufficient conditions for stability and asymptotic stability of the given systems based on Filippov differential inclusion and Clarke's generalized gradient are given.Finally,these results are illustrated by the given example.

Outlier-resistant distributed fusion filtering for nonlinear discrete-time singular systems under a dynamic event-triggered scheme

This paper investigates the problem of outlier-resistant distributed fusion filtering(DFF)for a class of multi-sensor nonlinear singular systems(MSNSSs)under a dynamic event-triggered scheme(DETS).To relieve the effect of measurement outliers in data transmission,a self-adaptive saturation function is used.Moreover,to further reduce the energy consumption of each sensor node and improve the efficiency of resource utilization,a DETS is adopted to regulate the frequency of data transmission.For the addressed MSNSSs,our purpose is to construct the local outlier-resistant filter under the effects of the measurement outliers and the DETS;the local upper bound(UB)on the filtering error covariance(FEC)is derived by solving the difference equations and minimized by designing proper filter gains.Furthermore,according to the local filters and their UBs,a DFF algorithm is presented in terms of the inverse covariance intersection fusion rule.As such,the proposed DFF algorithm has the advantages of reducing the frequency of data transmission and the impact of measurement outliers,thereby improving the estimation performance.Moreover,the uniform boundedness of the filtering error is discussed and a corresponding sufficient condition is presented.Finally,the validity of the developed algorithm is checked using a simulation example.

Interval Type-2 Fuzzy Passive Filtering for Nonlinear Singularly Perturbed PDT-Switched Systems and Its Application

The problem of designing a passive filter for nonlinear switched singularly perturbed systems with parameter uncertainties is explored in this paper.Firstly,the multiple-time-scale phenomenon is settled effectively by introducing a singular perturbation parameter in the plant.Secondly,the interval type-2 fuzzy set theory is employed where parameter uncertainties are expressed in membership functions rather than the system matrices.It is worth noting that interval type-2 fuzzy sets of the devised filter are different from the plant,which makes the design of the filter more flexible.Thirdly,the persistent dwell-time switching rule,as a kind of time-dependent switching rules,is used to manage the switchings among nonlinear singularly perturbed subsystems,and this rule is more general than dwell-time and average dwell-time switching rules.Next,sufficient conditions are provided for guaranteeing that the filtering error system is globally uniformly exponentially stable with a passive performance.Furthermore,on the basis of the linear matrix inequalities,the explicit expression of the designed filter can be obtained.Finally,a tunnel diode electronic circuit is rendered as an example to confirm the correctness and the validity of the developed filter.

The Improved Modified Decomposition Method for the Treatment of Systems of Singular Nonlinear Partial Differential Equations with Initial Conditions

New developed inverse differential operators incorporated into the semi- analytical treatment of the modified decomposition method （MDM） are used to solve the systems of first and second-order singular nonlinear partial differential equations （PDEs） with initial conditions arising in physics. The new proposed method is called the improved modified decomposition method （IMDM）, and is used to the treatment of a few case study initial-value problems. The results obtained by the IMDM are in full agreement with the existing exact analytical solutions.