Robust Impulsive Stabilization of Uncertain Nonlinear Singular Systems with Application to Transportation Systems

Abstract

We consider the robust asymptotical stabilization problem for uncertain singular systems. We design a new impulsive control technique to ensure that the controlled singular system is robustly asymptotically stable and hence derive the corresponding stability criteria. These sufficient conditions are expressed in the form of algebra matrix inequalities and can be implemented numerically. We finally provide a numerical example of a transportation system to illustrate the effectiveness and usefulness of the proposed criteria.

Eigenvalue Based Approach for Assessment of Global Robustness of Nonlinear Dynamical Systems

“…What can we say about the asymptotic behavior (as t → ∞) of solutions of perturbed system (1)? This question represents one of the fundamental problems in the area of robust stability and robustness of the systems in general and so the effect of (known or unknown) perturbations on the solutions of nominal system as a potential source of instability attracts the attention and interest of scientific community for a long time in the various contexts, recently for example [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. A comprehensive overview of the most significant results on robust control theory as a stand-alone subfield of control theory and its history is presented in [17,18].…”