Robust stabilization of linear uncertain discrete-time systems via a limited capacity communication channel

Channel signal-to-noise ratio constrained feedback control: performance and robustness

“…Robustness has been recently studied by means of information theoretic arguments in [10,Theorem 3.4] and in [11,Theorem 3.3] and in the context of quantised systems in [12,Theorem 2]. In [10,Theorem 3.4] an upper bound on the plant state mth moment is presented as a sufficient condition for the existence of a stabilising feedback for a discrete-time stochastic scalar plant subject to uncertainties and a communication channel with a stochastic transmission data rate.…”

“…In [10,Theorem 3.4] an upper bound on the plant state mth moment is presented as a sufficient condition for the existence of a stabilising feedback for a discrete-time stochastic scalar plant subject to uncertainties and a communication channel with a stochastic transmission data rate. In [11], on the other hand, a necessary condition is introduced for the stabilisability (and observability) of a linear discrete-time stochastic plant (subject to frequency-bounded uncertainties) as a lower bound on the channel capacity [11,Theorem 3.3], which is then explicitly computed for a scalar plant [11 [6,Theorem 7.3]) and the difficulty of implementing usually nonlinear solutions for the encoder and decoder involved in the communication channel [3,11,12]. Moreover, most of the contributions in the area of control over networks are for discrete-time systems.…”

Robust stabilization for a class of nonlinear networked control systems

“…Since Z > 0, it follows that for all τ k satisfying 0 < τ k τ k , Φ(τ k ) < 0 is equivalent to (10) in sense of the Schur complement.…”

“…Few results in robust stabilization problems for uncertain or nonlinear NCSs have been presented in the past years [9∼11]. In the discrete context, the state feedback robust stabilization problem for uncertain discrete-time systems via a limited capacity channel is discussed in [10], while in the continuous context, a robust H ∞ controller was designed and the MATI was derived in [11]. For a nonlinear nominal NCS, a two-step design approach is proposed, using standard control methodologies and choosing the network protocol in order to ensure that important closed-loop properties are preserved when a computer network is inserted into the feedback loop [9].…”

Robust output feedback stabilization of nonlinear networked systems via a finite data-rate communication channel

“…As a result, using feedback signals transmitted through a finite data-rate communication channel can have an adverse effect on the performance of the closed-loop system. In terms of stability performance, a number of control schemes and algorithms have been developed to recover the stability performance with feedback signals transmitted via a finite data-rate communication channel (see, e.g., [3][4][5][6][7]). Recently, there is a growing attention on stabilizing nonlinear systems with feedbacks via finite data-rate or limited capacity communication channels.…”