A Vector Small-Gain Theorem for General Nonlinear Control Systems

Abstract

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.

Submitted to IEEE Transactions on Automatic Control

Cited by in corpus (6)

• New Results in Trajectory-Based Small-Gain with Application to the Stabilization of a Chemostat
• Global stabilization of nonlinear systems based on vector control lyapunov functions
• Input-to-state stability of interconnected hybrid systems
• Stability verification for monotone systems using homotopy algorithms
• Stabilization by Means of Approximate Predictors for Systems with Delayed Input
• Reduction of the small gain condition for large-scale interconnections