On the Design of Output Feedback Controllers for LTI Systems Over Fading Channels

This paper considers linear time-invariant control systems over fading channels in both continuous-time and discrete-time cases and addresses the design of output feedback controllers that stabilize the closed-loop system in the mean square sense. It is shown that a sufficient and necessary condition for the existence of such controllers can be obtained by solving a convex optimization problem in the form of a semidefinite program. This condition is obtained by reformulating mean square stability as asymptotical stability of a suitable matrix comprising plant, controller, and channel, and by introducing modified Hurwitz and Schur stability criteria

Robust stability of uncertain linear systems with input and output quantization and packet loss

This paper investigates the robust stability of uncertain discrete-time linear systems subject to input and output quantization and packet loss. First, a necessary and sufficient condition in terms of LMIs is proposed for the quadratic stability of the closed-loop system with double quantization and norm bounded uncertainty in the plant. Moreover, it is shown that the proposed condition can be exploited to derive the coarsest logarithmic quantization density under which the uncertain plant can be quadratically stabilized via quantized state feedback. Second, a new class of Lyapunov function which depends on the quantization errors in a multilinear way is developed to obtain less conservative results. Lastly, the case with input and output packet-loss channels is investigated.<br

Robust Stability Analysis and Synthesis for Uncertain Discrete-Time Networked Control Systems Over Fading Channels

This technical note investigates uncertain discrete-time networked control systems over fading channels. It is assumed that the plant is affected by polytopic uncertainty and is connected to the controller in closed-loop via fading channels which are modeled by multiplicative noise processes. Three contributions are proposed as follows. First, it is shown that robust stability in the mean square sense of the uncertain closed-loop networked control system is equivalent to the existence of a Lyapunov function in a certain class. Second, it is shown that the existence of a Lyapunov function in such a class is equivalent to the feasibility of a set of linear matrix inequalities (LMIs). Third, it is shown that the proposed condition can be exploited for the synthesis of robust controllers ensuring robust stability in the mean square sense of the uncertain closed-loop networked control system

Consensus of Heterogeneous Multi-Agent Systems With Diffusive Couplings via Passivity Indices

This letter is concerned with the problem of output consensus for two classes of heterogeneous nonlinear multi-agent systems which are interconnected via diffusive couplings over directed graphs. Specifically, for agents that are input feed forward passive (IFP), a condition in terms of passivity indices is proposed for asymptotic output consensus. Moreover, it is shown that the proposed condition can be exploited to design the coupling gain that ensures asymptotic consensus via a semi definite program, and the existence of such a coupling gain can be guaranteed provided all the agents are IFP. For agents that are input feed forward output feedback passive, a condition in terms of passivity indices for practical output consensus is provided, in which the relationship between the coupling gain and the consensus error bound is revealed

Stabilization of Linear Systems Across a Time-Varying AWGN Fading Channel

This technical note investigates the minimum average transmit power required for mean-square stabilization of a discrete-time linear process across a time-varying additive white Gaussian noise (AWGN) fading channel that is presented between the sensor and the controller. We assume channel state information at both the transmitter and the receiver, and allow the transmit power to vary with the channel state to obtain the minimum required average transmit power via optimal power adaptation. We consider both the case of independent and identically distributed fading and fading subject to a Markov chain. Based on the proposed necessary and sufficient conditions for mean-square stabilization, we show that the minimum average transmit power to ensure stabilizability can be obtained by solving a geometric program

Distributed Resource Allocation over Time-varying Balanced Digraphs with Discrete-time Communication

This work is concerned with the problem of distributed resource allocation in continuous-time setting but with discrete-time communication over infinitely jointly connected and balanced digraphs. We provide a passivity-based perspective for the continuous-time algorithm, based on which an intermittent communication scheme is developed. Particularly, a periodic communication scheme is first derived through analyzing the passivity degradation over output sampling of the distributed dynamics at each node. Then, an asynchronous distributed event-triggered scheme is further developed. The sampled-based event-triggered communication scheme is exempt from Zeno behavior as the minimum inter-event time is lower bounded by the sampling period. The parameters in the proposed algorithm rely only on local information of each individual node, which can be designed in a truly distributed fashion