Robust stability of systems with application to singular perturbations

In this paper we will give a simple approach to determining conditions for stability of feedback systems subject to perturbations in the operators describing these systems. The approach is based on techniques used in functional analysis, and provides an alternative development and generalization of some conditions for the linear time-invariant case that have appeared in the literature very recently. As an example of the application of the conditions, we consider the determination of finite regions of stability for singularly perturbed systems.

[1]  Petar V. Kokotovic,et al.  Singular perturbations and order reduction in control theory - An overview , 1975, at - Automatisierungstechnik.

[2]  Jan C. Willems,et al.  The Analysis of Feedback Systems , 1971 .

[3]  Michael Athans,et al.  Gain and phase margin for multiloop LQG regulators , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[4]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[5]  P. Kokotovic,et al.  Control strategies for decision makers using different models of the same system , 1978 .

[6]  Michael Athans,et al.  Survey of decentralized control methods for large scale systems , 1978 .

[7]  J. Doyle Robustness of multiloop linear feedback systems , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[8]  Jack J. Dongarra,et al.  Matrix Eigensystem Routines — EISPACK Guide Extension , 1977, Lecture Notes in Computer Science.

[9]  C. Desoer,et al.  Networks with very small and very large parasitics: Natural frequencies and stability , 1970 .

[10]  A. Laub LINEAR MULTIVARIABLE CONTROL. NUMERICAL CONSIDERATIONS. , 1978 .