Feedback Stability Analysis via Dissipativity with Dynamic Supply Rates

In this paper, we propose a notion of dissipativity with dynamic supply rates for nonlinear differential input-state-output equations via the use of auxiliary systems. This extends the classical dissipativity with static supply rates and miscellaneous dynamic quadratic forms. The main results of this paper concern Lyapunov (asymptotic/exponential) stability analysis for nonlinear feedback dissipative systems that are characterised by dissipation inequalities with respect to compatible dynamic supply rates. Importantly, dissipativity conditions guaranteeing partial stability of the state of the feedback systems without concerning that of the state of the auxiliary systems are provided. They are shown to recover several existing results in the literature. Comparison with the input-output approach to feedback stability analysis based on integral quadratic constraints is also made

Localization of Control Synthesis Problem for Large-Scale Interconnected System Using IQC and Dissipativity Theories

The synthesis problem for the compositional performance certification of interconnected systems is considered. A fairly unified description of control synthesis problem is given using integral quadratic constraints (IQC) and dissipativity. Starting with a given large-scale interconnected system and a global performance objective, an optimization problem is formulated to search for admissible dissipativity properties of each subsystems. Local control laws are then synthesized to certify the relevant dissipativity properties. Moreover, the term localization is introduced to describe a finite collection of syntheses problems, for the local subsystems, which are a feasibility certificate for the global synthesis problem. Consequently, the problem of localizing the global problem to a smaller collection of disjointed sets of subsystems, called groups, is considered. This works looks promising as another way of looking at decentralized control and also as a way of doing performance specifications for components in a large-scale system