The problem of controlling multiple scalar systems through a limited capacity shared channel is considered. Each system is affected by process noise and can be controlled by actuators with values in a fixed finite set. The control objective is to bound the evolution of the systems in specified sets (controlled invariance). The goal is to find an optimal allocation of the shared communication resource to the different control activities and to identify correct choices for the design parameters. A feasibility criterion is given to decide whether a set of design parameters conforms with a control specification. The explicit computation of the minimum bit rate necessary for the controlled invariance of a set is also provided. The analysis is restricted to scalar systems ruled by control laws generated by periodic sampling and uniform quantizers. The subset U necessary to accomplish the control task is a design parameter along with the sampling period. The investigation focuses on the steady-state behavior of the system, i.e., the ability to make a desired set invariant. The presence of noise is of particular interest, as it emphasizes the importance of the sampling period, especially for unstable systems. The paper provides fundamental conceptual tools to attack the design problem in the formal framework of an optimization problem. The design problem for a single loop is thoroughly investigated, and two fundamental questions are addressed: the identification of the feasible design parameters with respect to a control specification and the determination of the minimum bit rate necessary to attain a specification. The analysis is based on the assumption that control loops are operated by quantized actuators, which are regarded as given "hardware" components. The general setting is depicted in a figure, where a limited bandwidth channel is shared between several independent control loops. The investigation is restricted to a "smart-sensor" scenario, where processing activities are located in the proximity of sensors and commands have to be sent to actuators by a channel. The analysis is based on the assumption that the control function takes values in a regularly quantized set. The sampled-data control system corresponding to the given parameters is derived, and the discrete time disturbance is expressed in terms of the given parameters. The quantized discrete time control law is a function that maps the state of the system to a control value in the quantized set. The analysis is based on the assumption that the control law is a function that maps the state of the system to a control value in the quantized set. The investigation focuses on the steady-state behavior of the system, i.e., the ability to make a desired set invariant. The presence of noise is of particular interest, as it emphasizes the importance of the sampling period, especially for unstable systems. The paper provides fundamental conceptual tools to attack the design problem in the formal framework of an optimization problem. The design problem for a single loop is thoroughly investigated, and two fundamental questions are addressed: the identification of the feasible design parameters with respect to a control specification and the determination of the minimum bit rate necessary to attain a specification. The analysis is based on the assumption that control loops are operated by quantized actuators, which are regarded as given "hardware" components. The general setting is depicted in a figure, where a limited bandwidth channel is shared between several independent control loops. The investigation is restricted to a "smart-sensor" scenario, where processing activities are located in the proximity of sensors and commands have to be sent to actuators by a channel. The analysis is based on the assumption that the control function takes values in a regularly quantized set. The sampled-data control system corresponding to the given parameters is derived, and the discrete time disturbance is expressed in terms of the given parameters. The quantized discrete time control law is a function that maps the state of the system to a control value in the quantized set. The investigation focuses on the steady-state behavior of the system, i.e., the ability to make a desired set invariant. The presence of noise is of particular interest, as it emphasizes the importance of the sampling period, especially for unstable systems. The paper provides fundamental conceptual tools to attack the design problem in the formal framework of an optimization problem. The design problem for a single loop is thoroughly investigated, and two fundamental questions are addressed: the identification of the feasible design parameters with respect to a control specification and the determination of the minimum bit rate necessary to attain a specification. The analysis is based on the assumption that control loops are operated by quantized actuators, which are regarded as given "hardware" components. The general setting is depicted in a figure, where a limited bandwidth channel is shared between several independent control loops. The investigation is restricted to a "smart-sensor" scenario, where processing activities are located in the proximity of sensors and commands have to be sent to actuators by a channel. The analysis is based on the assumption that the control function takes values in a regularly quantized set. The sampled-data control system corresponding to the given parameters is derived, and the discrete time disturbance is expressed in terms of the given parameters. The quantized discrete time control law is a function that maps the state of the system to a control value in the quantized set. The investigation focuses on the steady-state behavior of the system, i.e., the ability to make a desired set invariant. The presence of noise is of particular interest, as it emphasizes the importance of the sampling period, especially for unstable systems. The paper provides fundamental conceptual tools to attack the design problem in the formal framework of an optimization problem. The design problem for a single loop is thoroughly investigated, and two fundamental questions are addressed: the identification of the feasible design parameters with respect to a control specification and the determination of the minimum bit rate necessary to attain a specification. The analysis is based on the assumption that control loops are operated by quantized actuators, which are regarded as given "hardware" components. The general setting is depicted in a figure, where a limited bandwidth channel is shared between several independent control loops. The investigation is restricted to a "smart-sensor" scenario, where processing activities are located in the proximity of sensors and commands have to be sent to actuators by a channel. The analysis is based on the assumption that the control function takes values in a regularly quantized set. The sampled-data control system corresponding to the given parameters is derived, and the discrete time disturbance is expressed in terms of the given parameters. The quantized discrete time control law is a function that maps the state of the system to a control value in the quantized set. The investigation focuses on the steady-state behavior of the system, i.e., the ability to make a desired set invariant. The presence of noise is of particular interest, as it emphasizes the importance of the sampling period, especially for unstable systems. The paper provides fundamental conceptual tools to attack the design problem in the formal framework of an optimization problem. The design problem for a single loop is thoroughly investigated, and two fundamental questions are addressed: the identification of the feasible design parameters with respect to a control specification and the determination of the minimum bit rate necessary to attain a specification. The analysis is based on the assumption that control loops are operated by quantized actuators, which are regarded as given "hardware" components. The general setting is depicted in a figure, where a limited bandwidth channel is shared between several independent control loops. The investigation is restricted to a "smart-sensor" scenario, where processing activities are located in the proximity of sensors and commands have to be sent to actuators by a channel. The analysis is based on the assumption that the control function takes values in a regularly quantized set. The sampled-data control system corresponding to the given parameters is derived, and the discrete time disturbance is expressed in terms of the given parameters. The quantized discrete time control law is a function that maps the state of the system to a control value in the quantized set. The investigation focuses on the steady-state behavior of the system, i.e., the ability to make a desired set invariant. The presence of noise is of particular interest, as it emphasizes the importance of the sampling period, especially for unstable systems. The paper provides fundamental conceptual tools to attack the design problem in the formal framework of an optimization problem. The design problem for a single loop is thoroughly investigated, and two fundamental questions are addressed: the identification of the feasible design parameters with respect to a control specification and the determination of the minimum bit rate necessary to attain a specification. The analysis is based on the assumption that control loops are operated by quantized actuators, which are regarded as given "hardware" components. The general setting is depicted in a figure, where a limited bandwidth channel is shared between several independent control loops. The investigation is restricted to a "smart-sensor" scenario, where processing activities are located in the proximity of sensors and commands have to be sent to actuators by a channel. The analysis is based on the assumption that the control function takes values in a regularly quantized set. The sampled-data control system corresponding to the given parameters is derived, and the discrete time disturbance is expressed in terms of the given parameters. The quantized discrete time control law is a function that maps the state of the system to a control value in the quantized set. The investigation focuses on the steady-state behavior of the system, i.e., the ability to make a desired set invariant. The presence of noise is of particular interest, as it emphasizes the importance of the sampling period, especially for unstable systems. The paper provides fundamental conceptual tools to attack the design problem in the formal framework of an optimization problem. The design problem for a single loop is thoroughly investigated, and two fundamental questions are addressed: the identification of the feasible design parameters with respect to a control specification and the determination of the minimum bit rate necessary to attain a specification. The analysis is based on the assumption that control loops are operated by quantized actuators, which are regarded as given "hardware" components. The general setting is depicted in a figure, where a limited bandwidth channel is shared between several independent control loops. The investigation is restricted to a "smart-sensor" scenario, where processing activities are located in the proximity of sensors and commands have to be sent to actuators by a channel. The analysis is based on the assumption that the control function takes values in
