A Remark on an Example By Teel-Hespanha With Applications to Cascaded Systems

• Published in: IEEE transactions on automatic control Vol. 52; no. 2; pp. 289 - 293
• Main Author: Astolfi, A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-02-2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Automatic control; Cascaded systems; Computer science; control theory; systems; Control theory. Systems; Decay; Displays; Disturbances; Exact sciences and technology; H infinity control; History; Infinity; Nonlinear equations; Nonlinear systems; Predictive models; Simulation; Stability; Sufficient conditions; Trajectories; Non linear control; nonlinear systems; Cascaded systems; Exponential stability; Cascade systems; stability
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2006.889870

The properties of a system, proposed by Teel and Hespanha, which is globally exponentially stable but with state that can be driven to infinity by an arbitrarily small exponentially decaying disturbance, are discussed in detail. These are used to propose a family of systems with a similar property and to argue that unstable behavior may be nongeneric and not detected by means of simulations. Finally, sufficient conditions for the existence of unbounded trajectories in cascaded systems are given