A Vector Small-Gain Theorem for General Nonlinear Control Systems

Details A Vector Small-Gain Theorem for General Nonlinear Control Systems A Vector Small-Gain Theorem for General Nonlinear Control Systems

2009-04-05

arxiv.org/abs/0904.0755v1

Mathematics

Optimization and Control

Submitted to IEEE Transactions on Automatic Control

Scientific paper

A new Small-Gain Theorem is presented for general nonlinear control systems. The novelty of this research work is that vector Lyapunov functions and functionals are utilized to derive various input-to-output stability and input-to-state stability results. It is shown that the proposed approach recovers several recent results as special instances and is extendible to several important classes of control systems such as large-scale complex systems, nonlinear sampled-data systems and nonlinear time-delay systems. An application to a biochemical circuit model illustrates the generality and power of the proposed vector small-gain theorem.

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