TY - GEN
T1 - Storage functions for dissipative linear systems are quadratic state functions
AU - Trentelman, HL
AU - Willems, JC
PY - 1997
Y1 - 1997
N2 - This paper deals with dissipative dynamical systems. Dissipative dynamical systems can be used as models for physical phenomena in which energy exchange with their environment plays a role. In a dissipative dynamical system, the book-keeping of energy is done via the supply rate and a storage function. The supply rate is the rate at which energy flows into the system, a storage function is a function that measures the amount of enery that is stored inside the system. In this paper, we will argue that for linear dynamical systems with quadratic supply rates, any storage function can be represented as a quadratic function of any state variable of a linear dynamical system whose dynamics is obtained by combining the dynamics of the original system, and the dynamics of the supply rate.
AB - This paper deals with dissipative dynamical systems. Dissipative dynamical systems can be used as models for physical phenomena in which energy exchange with their environment plays a role. In a dissipative dynamical system, the book-keeping of energy is done via the supply rate and a storage function. The supply rate is the rate at which energy flows into the system, a storage function is a function that measures the amount of enery that is stored inside the system. In this paper, we will argue that for linear dynamical systems with quadratic supply rates, any storage function can be represented as a quadratic function of any state variable of a linear dynamical system whose dynamics is obtained by combining the dynamics of the original system, and the dynamics of the supply rate.
M3 - Conference contribution
SN - 0-7803-4187-2
T3 - IEEE CONFERENCE ON DECISION AND CONTROL - PROCEEDINGS
SP - 42
EP - 47
BT - PROCEEDINGS OF THE 36TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5
PB - IEEE (The Institute of Electrical and Electronics Engineers)
CY - NEW YORK
T2 - 36th IEEE Conference on Decision and Control
Y2 - 10 December 1997 through 12 December 1997
ER -