Stabilization of Singularly Perturbed Systems

Abstract

Stability analysis and controller design are significant problems of dynamic systems in theory and practice that have attracted the interest of many investigators [4]. In recent decades, researchers have focused on the problem of stability analysis and stabilization for SPSs, and these approaches can improve the control precision of system. In this chapter, we first discuss the concept of stability in general, and then present four techniques for assessing the stability of a system: (1) introducing Lyapunov functions; (2) finding the eigenvalues for state-space notation; (3) finding the location of the poles in the complex frequency plane of the closed-loop TF; and (4) providing a descriptor-system method to stabilize the SPSs. Note that the stability of the system should be guaranteed in the entire frequency range, while the related control system specifications should be specified in the finite frequency ranges to reduce their conservatism.