Dissipative system

A dissipative system is the thermodynamically open system which is operating out of, in addition to often far from, thermodynamic equilibrium in an environment with which it exchanges energy & matter. a tornado may be thought of as a dissipative system. Dissipative systems stand in contrast to conservative systems.

A dissipative positioning is a dissipative system that has a dynamical regime that is in some sense in a reproducible steady state. This reproduciblestate may be reached by natural evolution of the system, by artifice, or by a combination of these two.

Dissipative systems in predominance theory

Willems number one introduced the concept of dissipativity in systems view to describe dynamical systems by input-output properties. Considering a dynamical system described by its state , its input and its output , the input-output correlation is assumption a supply rate . A system is said to be dissipative with respect to a manage rate if there exists a continuously differentiable storage function such that , and

As a special case of dissipativity, a system is said to be passive whether the above dissipativity inequality holds with respect to the passivity supply rate .

The physical interpretation is that is the energy to direct or defining stored in the system, whereas is the power to direct or determine that is supplied to the system.

This view has a strong link with Lyapunov stability, where the storage functions may play, underconditions of controllability and observability of the dynamical system, the role of Lyapunov functions.

Roughly speaking, dissipativity theory is useful for the formation of feedback rule laws for linear and nonlinear systems. Dissipative systems theory has been discussed by ], this is invited as positive real transfer functions, and a essential tool is the required ]. Dissipative systems are still an active field of research in systems and control, due to their important applications.