Dissipativity Properties of Nonlinear Systems Under Network Constraints

QSR‐dissipativity of feedback interconnection of switched nonlinear systems under communication constraints

“…As far as the feedback interconnected systems are concerned, the connection between subsystems is often made through communication links. For example, the output‐based event‐triggered control (OBETC) for feedback interconnected systems has been widely used in the study of stability, 4 dissipativity, 24‐29 stability 26‐28 . Compared with the continuous transmission channels, in practice, the communication constraints that can maintain the systems' properties are more frequent to be used for saving costs.…”

“…The first is that the transmission channels of two systems based on static output feedback 2 limit the choices of controllers and the systems do not have margin that depends only on outputs to trade off the effects when the state remains within the kernel spaces of outputs 4 . The second is that when the state approaches the origin, the exclusion of Zeno behavior becomes even more difficult because arbitrary exogenous inputs may lead to infinity triggers in a short period 29 . Namely, the difficulty lies on the exclusion of Zeno behavior since when the output approaches zero or is equal to zero but the state does not approach the origin, the number of samplings triggered by the event can reach infinity in a short time.…”

“…References 26‐28 remove the restriction and study the dissipativity problem under the condition that restricts disturbances to Sobolev spaces, that is, continuously differentiable signals with bounded derivative. In the background of dissipativity, we should point out that although these results 26‐28 under this restriction can indeed avoid Zeno behavior in finite time, it cannot however constrain the number of samplings over finite intervals and therefore may fail to serve the main purpose of a triggering system of limiting the information transmission between subsystems 29 . In order to relax the restriction, a novel OBETC is proposed in Reference 29 to study the dissipativity problem based on the assumption that each subsystem is input‐output‐to‐state stable (IOSS), where the storage function of feedback interconnected systems is the combination of the storage functions and the IOSS functions of lower‐dimension systems.…”

“…In the background of dissipativity, we should point out that although these results 26‐28 under this restriction can indeed avoid Zeno behavior in finite time, it cannot however constrain the number of samplings over finite intervals and therefore may fail to serve the main purpose of a triggering system of limiting the information transmission between subsystems 29 . In order to relax the restriction, a novel OBETC is proposed in Reference 29 to study the dissipativity problem based on the assumption that each subsystem is input‐output‐to‐state stable (IOSS), where the storage function of feedback interconnected systems is the combination of the storage functions and the IOSS functions of lower‐dimension systems. Note that the OBETC in Reference 29 not only guarantees dissipativity of systems, but also restricts the number of samplings over finite intervals by providing a unified positive lower bound of the interexecution times, that is, the event‐separation property.…”

“…In order to relax the restriction, a novel OBETC is proposed in Reference 29 to study the dissipativity problem based on the assumption that each subsystem is input‐output‐to‐state stable (IOSS), where the storage function of feedback interconnected systems is the combination of the storage functions and the IOSS functions of lower‐dimension systems. Note that the OBETC in Reference 29 not only guarantees dissipativity of systems, but also restricts the number of samplings over finite intervals by providing a unified positive lower bound of the interexecution times, that is, the event‐separation property. However, the IOSS assumption is quite restrictive for the systems with QSR‐dissipativity.…”