Stability Criteria For Singular Systems Research Articles

Improved Results on Stability Criteria for Singular Systems with Interval Time-Varying Delays

The purpose of this paper is to address the problem of assessing the stability of singular time-varying delay systems. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, a model transformation using a three-terms approximation of the delayed state is exploited. Based on the lifting method and the Lyapunov–Krasovskii functional (LKF) method, a new linear matrix inequality (LMI) is obtained, allowing conclusions on stability to be drawn using the scaled small gain theorem (SSG). The use of SSG theorem for stability of singular systems with time-varying delay has not been investigated elsewhere in the literature. This represents the main novelty of this article. The result is applicable for assessing the stability of both singular systems and neutral systems with time-varying delays. The less conservativeness of the stability test is illustrated by comparison with recent literature results.

The Input-output's Control Strategy of the Fashion Company

This paper deals with the problems of control strategy of the fashion company. The input-output model is founded based on the singular stochastic dynamic Leontief inputoutput model. A new mathematic method is applied to study the singular systems without converting them into general linear systems. The parameter uncertainties are considered and are assumed to be time-invariant and Markovian jumping. A new stability criterion for singular system is given to ensure the robust stability of singular input-output model in terms of linear matrix inequality. Finally, the corresponding computer control algorithm is provided.

New stability criteria for singular systems with time-varying delay and nonlinear perturbations

This paper concerns the stability analysis for singular systems with time-varying delay and nonlinear perturbations. Two cases of time-varying delay, which is differentiable (Case 1) or not differentiable (Case 2), are considered. The considered nonlinear perturbations includes the norm-bounded uncertainties as a special case. Some delay-dependent stability criteria are derived by using a delay decomposition approach. In the delay decomposition approach, the entire delay interval is divided into multiple sub-intervals for which different energy functions are defined for building new Lyapunov–Krasovskii functional. Some numerical and practical examples are given to show the effectiveness and significant improvement of the proposed method.

A Stability Criterion for Singular Systems with Two Additive Time- varying Delay Components

The problem of stability for singular systems with two additive time-varying delay components is investigated. By constructing a simple type of Lyapunov-Krasovskii functional and utilizing free matrix variables in approximating certain integral quadratic terms, a delay-dependent stability criterion is established for the considered systems to be regular, impulse free, and stable in terms of linear matrix inequalities (LMIs). Based on this criterion, some new stability conditions for singular systems with a single delay in a range and regular systems with two additive time-varying delay components are proposed. These developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism. Finally, two numerical examples are employed to illustrate the effectiveness of the obtained theoretical results.

Delay‐Dependent Stability Criteria for Singular Systems with Interval Time‐Varying Delay

This paper is concerned with stability analysis for singular systems with interval time‐varying delay. By constructing a novel Lyapunov functional combined with reciprocally convex approach and linear matrix inequality (LMI) technique, improved delay‐dependent stability criteria for the considered systems to be regular, impulse free, and stable are established. The developed results have advantages over some previous ones as they involve fewer decision variables yet less conservatism. Numerical examples are provided to demonstrate the effectiveness of the proposed stability results.