×

zbMATH — the first resource for mathematics

Delay effects on stability. A robust control approach. (English) Zbl 0997.93001
Lecture Notes in Control and Information Sciences. 269. London: Springer. xvi, 383 p. (2001).
From the author’s preface: The monograph is devoted to the effect of delays on the stability properties of dynamical systems. Stability regions with respect to the delay parameters are considered, and some sufficient or necessary and sufficient characterizations are proposed.
In the first chapter, the problem statement, the definition of the state, the existence of solutions, uniqueness, continuous dependence, stability definitions, etc. are presented. In the second chapter some engineering and biological examples are considered. The third chapter is devoted to the basic delay effect, notions in delay systems and propagation models. The fourth chapter addresses the frequency-domain for the analysis of dynamical systems including discrete ones, or some special classes of distributed delays. The fifth chapter is devoted to Lyapunov’s second method and its application. The sixth chapter deals with some robustness issues in closed-loop schemes. The last chapter is devoted to some applications.

MSC:
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93C23 Control/observation systems governed by functional-differential equations
34K20 Stability theory of functional-differential equations
93D15 Stabilization of systems by feedback
93D09 Robust stability
93C55 Discrete-time control/observation systems
34K40 Neutral functional-differential equations
34K06 Linear functional-differential equations
PDF BibTeX XML Cite