ABSTRACT
This book has presented recent results on the stability and control of interconnected systems which are modeled as dynamic networks. Such networks arise naturally in engineering applications, such as robotic networks and power systems, as well as in other areas such as biology, physics, and economics. The treatment is all based on the concept of input-to-state stability (ISS) and the idea of small-gain in loops of the network as a means to achieve stability when systems are interconnected. The ISS property for each subsystem includes nonlinear gain functions and corresponds to the existence of an ISS-Lyapunov function. The stability conditions are intuitively and conveniently expressed in terms of compositions of the gains associated with cycles in the system graph being less than one, generalizing the well-known small-gain theorem for feedback systems. After establishing the small-gain theorems for classes of dynamic networks (continuous-time, discrete-time, and hybrid), the book proposed a set of tools for input-to-state stabilization and robust control of complex nonlinear systems from the viewpoint of dynamic networks. Among these tools and applications are:
• Lyapunov-based cyclic-small-gain theorems for continuous-time, discrete-time, and hybrid dynamic networks composed of multiple ISS subsystems;
• novel small-gain-based static feedback and dynamic feedback designs for robust control of nonlinear uncertain systems with disturbed measurements;
• quantized stabilization designs for nonlinear uncertain systems with static quantization and dynamic quantization; and
• distributed coordination control of nonlinear multi-agent systems under information exchange constraints.
