Passivity technique in control and network synthesis of descriptor systems

In this paper, we derive the necessary and sufficient conditions for generalized state space (or descriptor) systems to be ESPR (Extended Strictly Positive Real). The result concerns a generalized algebraic Riccati equation (GARE). This technique is then applied to the ESPR control problems for descriptor systems. Both state feedback and output feedback cases are examined. In addition, a parameterization of ESPR state feedback controllers is also obtained. Finally, we consider the problem of synthesizing a reciprocal positive real network in the generalized state space. This problem is fairly conceptual but has particular importance in discussing the time reversiblity of a dynamical system.