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Control with general dissipativity constraint and non-monotonic Lyapunov functions

In this paper, a new framework for constructing discrete-time control systems with non-monotonic Lyapunov functions and General Dissipativity Constraint (GDC) is developed as an alternative to the small gain design that may become conservative in some decentralized control applications. The GDC Lyapunov function in this approach is nonmonotonic since its incremental difference is essentially nonnegative. Possessing the advantages of an input and output approach, the presented GDC is suitable for the control problem of heterogeneous interconnected systems that have complex interactions between subsystems, such as power systems or networked robotics.