Robustness analysis of descriptor systems with parameter uncertainties

Abstract

This paper investigates the problem of robustness analysis for descriptor systems with parameter uncertainties in both the derivative and state matrices. Using a parameter dependent Lyapunov function, we derive a linear matrix inequality (LMI) based sufficient condition for the admissibility of the system. Unlike the existing results, our criterion has no restriction on the rank of the derivative matrix. Further, we use the obtained method to study interval descriptor systems and multi-parameter singular perturbed systems. The proposed approaches overcome some drawbacks of the existing results. Finally, we present two numerical examples to show the effectiveness of the main results.

Finite-time stability analysis and controller synthesis for switched linear parameter-varying systems

“…Considering the definition of Q i (v), the (30) is equivalent to (9), which implies that (26) and (27) are the sufficient conditions for (9). At last, based on the definition of Q i (v), the following equations are obtained: …”

“…tational burden [9]. Motivated by the above analysis, in this paper, we address the problem of finite-time stability analysis and controller synthesis for switched linear parameter-varying (LPV) systems.…”

Robust stability and stabilization for descriptor systems with uncertainties in all matrices

“…However, the 2 systems will have the same impulsive behavior, it has to require that the original system be normalized by the derivative state feedback. Some other results about the quadratic stability and stabilization can be found in the works of Zhang and Zhang, Teng et al, and Ren and Zhang and in previous works, some results of robust H ∞ control for the uncertain descriptor systems have also been studied. Among these references mentioned above, investigated the situation that no restriction is imposed on the rank of the derivative matrix E .…”

“…Under the same constraint of the derivative matrix E, stability and stabilization problems for interval descriptor system were discussed in the work of Lin et al 15 Then, due to the efficiency of the liner matrix inequality (LMI) technique in dealing with many problems of practical systems, 16,17 some well-studied results were developed for LMI-based ones for the descriptor systems. [18][19][20][21][22][23][24][25][26][27][28] There was a good idea proposed in the work of Lin et al, 18 in which, the problem of quadratic normalization and stabilization via a proportional and derivative state feedback was solved by transforming it into a corresponding stabilization problem of an augmented uncertain descriptor system. However, the 2 systems will have the same impulsive behavior, it has to require that the original system be normalized by the derivative state feedback.…”

Robust decentralized stabilization of large-scale singular systems via proportional-plus-derivative state feedback

“…In practice, the structure and behavior of a singular system are directly related to the derivative matrix E , which, as the other system matrix in the state space description, is subjected to possible time-varying or perturbations [2]. As to the problem of controller design for singular systems, there are usually two ways: one is the regularization problem, about which proportional plus derivative controller is used to make the closed-loop systems nonsingular and stable, see [3], [4], [5] and the references therein. Another is the stabilization problem, and a pure proportional controller is designed such that the closed system is regular, impulse-free (causal) and stable.…”