Dissipative Systems

We shall study a special class of systems called dissipative systems. Intuitively, we can think of systems interacting with the surrounding via some input / output ports, exchanging power with the surrounding, storing some energy and dissipating some. For example, electrical systems exchange power with the surrounding via an inner product between the current and voltage, i.e., Pe = v i. Energy in these systems may be stored in capacitors and/or inductors in the form of voltage or current, respectively. Another example is mechanical systems; these systems may by supplied with linear and/or rotational power, i.e., Pm = ωT or Pm = vF , where v is the velocity, F is the applied force, ω is the rotational speed, and T is the applied torque. This supply may be stored in the form of potential and/or kinetic energy. In what follows, we shall provide a solid foundation for such supply and storage concepts that allows us to describe systems from an input-output perspective.