NCS Model and Problem Statement Sample Clauses

NCS Model and Problem Statement. In the following we describe a NCS that includes unknown time-varying sampling intervals and un- known time-varying delays. A schematic of the considered NCS is shown in Fig. 16. It consists of a linear continuous-time plant x˙(t) = Ax(t) + Bu(t) (138) ∈ ∈ with A Rnx×nx and B Rnx×nu , and a discrete-time controller, connected over a communication network that induces network delays, namely the sensor-to-controller delay τ sc and the controller-to- actuator delay τ ca. A complete measurement of the state vector x(t) is assumed to be available at the sampling time instants Σ i s = k—1 h 6k ≥ 1, s0 = 0, (139) ∈ which may not be equidistantly spaced in time due to the time-varying sampling intervals hk > 0. The sequence s0, s1, s2, . . . is assumed to be strictly increasing, i.e., sk+1 > sk, for all k N. We denote by xk = x(sk) the kth sampled value of the state x and by uk the corresponding control value. The zero-order-hold (ZOH) function in Fig. 16 transforms the discrete-time control input uk to the continuous-time control input u(t) applied to the plant.