Robust stabilization of singular-impulsive-delayed systems with nonlinear perturbations

Many dynamic systems in physics, chemistry, biology, engineering, and information science have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical process, and these complex dynamic behaviors can be modeled by singular impulsive differential systems. This paper formulates and studies a model for singular impulsive delayed systems with uncertainty from nonlinear perturbations. Several fundamental issues such as global exponential robust stabilization of such systems are established. A simple approach to the design of a robust impulsive controller is then presented. A numerical example is given for illustration of the theoretical results. Meanwhile, some new results and refined properties associated with the M-matrices and time-delay dynamic systems are derived and discussed.

[1]  Charles O’Neill.  APPLICATIONS OF OPERATIONAL AMPLIFIERS , 2000 .

[2]  Shin-Ju Chen,et al.  Robustness analysis of uncertain linear singular systems with output feedback control , 1999, IEEE Trans. Autom. Control..

[3]  J. Chou,et al.  Stability robustness of continuous-time perturbed descriptor systems , 1999 .

[4]  Yuanqing Li,et al.  Bifurcation on stability of singular systems with delay , 1999, Int. J. Syst. Sci..

[5]  Arkadiĭ Khaĭmovich Gelig,et al.  Stability and Oscillations of Nonlinear Pulse-Modulated Systems , 1998 .

[6]  Mohamad Adnan Al-Alaoui.  A differential integrator with a built-in high-frequency compensation , 1998 .

[7]  Mohamad Adnan Al-Alaoui.  A stable inverting integrator with an extended high-frequency range , 1998 .

[8]  Yongqing Liu,et al.  Stability for composite singular systems of differential equations with a delay , 1996 .

[9]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[10]  Wei-Yong Yan,et al.  On initial instantaneous jumps of singular systems , 1995, IEEE Trans. Autom. Control..

[11]  Zhi-Hong Guan,et al.  Decentralized stabilization of singular and time-delay large-scale control systems with impulsive solutions , 1995, IEEE Trans. Autom. Control..

[12]  Zhi-Hong Guan,et al.  The application of auxiliary simultaneous equations to the problem in the stabilization of singular and impulsive large scale systems , 1995 .

[13]  Frank L. Lewis,et al.  A tutorial on the geometric analysis of linear time-invariant implicit systems , 1992, Autom..

[14]  Mohamad Adnan Al-Alaoui.  A novel differential differentiator , 1991 .

[15]  J. Aplevich.  Implicit Linear Systems , 1991 .

[16]  Stephen L. Campbell,et al.  Descriptor systems in the 1990s , 1990, 29th IEEE Conference on Decision and Control.

[17]  M. A. Al-Aaoui.  A novel approach to designing a noninverting integrator with built-in low frequency stability, high frequency compensation, and high Q , 1989 .

[18]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[19]  Andrew A. Goldenberg,et al.  Force and position control of manipulators during constrained motion tasks , 1989, IEEE Trans. Robotics Autom..

[20]  N. Harris McClamroch,et al.  Singular systems of differential equations as dynamic models for constrained robot systems , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[21]  F. Lewis.  A survey of linear singular systems , 1986 .

[22]  T. Mori,et al.  On an estimate of the decay rate for stable linear delay systems , 1982 .

[23]  S. G. Pandit,et al.  Differential systems involving impulses , 1982 .

[24]  T. Kailath,et al.  A generalized state-space for singular systems , 1981 .

[25]  R. Newcomb.  The semistate description of nonlinear time-variable circuits , 1981 .

[26]  Willis J. Tompkins,et al.  Design of Microcomputer-Based Medical Instrumentation , 1981 .

[27]  S. Campbell.  Singular Systems of Differential Equations , 1980 .

[28]  David H. Owens,et al.  Iterative solution of constrained differential/algebraic systems , 1978 .

[29]  M. Araki.  Stability of large-scale nonlinear systems--Quadratic-order theory of composite-system method using M-matrices , 1978 .

[30]  D. Luenberger.  Dynamic equations in descriptor form , 1977 .