Closed-loop Development for Dissipativity Constraint

The quadratic dissipativity constraint (QDC), a generalization of the asymptotically positive realness constraint (APRC), has previously been introduced and developed into an enforced stability constraint for the model predictive control schemes. This paper presents the novel development for a static constrained-state feedback control of interconnected systems, in which the decentralized QDC is employed for assuring the closed-loop stability of the global large-scale system. In this work, the input-and-power-to-state stability (IpSS), an extension of the input-to-state stability (ISS), is achieved. Under the realm of IpSS, the system stability does not rely on the monotonically reducing Lyapunov function. As a result, the proposed method provides a less conservative decentralized control law compared to those synthesized with the traditional Lyapunov stability condition. Simulation studies with small-signal linear models of three typical power systems are presented to demonstrate the effectiveness of the QDC, especially for systems having state constraints.