Stabilization of Arbitrary Switched Linear Systems With Unknown Time-Varying Delays

Stability analysis of networked control systems: A sum of squares approach

“…[5]- [7], [10], [11], [14], [25], [26], which applies to linear plants and linear controllers and is based on exact discretization of the NCS between two transmission times. After a polytopic overapproximation step, robust stability analysis methods are used to obtain LMI-based conditions for stability of the NCS.…”

Stability of networked control systems with large delays

“…Therefore, the matrices M and N will have different values within the different sampling intervals. This observation shows that (8), (10) or (8), (11) represent a switching discrete-time system. Then, the existence of a common quadratic Lyapunov function is indeed sufficient for the stability of (8), (10) or of (8), (11) for which the same reasoning holds.…”

“…For the sake of brevity, this additional analysis will not be considered. Therefore, the observation of a possible deadlock means that controller (10), as proposed in [10] for delays smaller than the sampling interval, does not function properly in the case of packet dropouts between the sensor and the controller (first case). The second controller (11) does not suffer from this problem as it only depends on the state x k (and not on the previous control inputs).…”

“…Most of the literature that deals with stability and stabilization of NCSs focuses either on packet dropouts [1], [8], [9] or on time-varying delays (see e.g. [1], [10], [11]). In [12] and [13] and stabilization of NCSs with packet dropouts and constant delays are investigated, based on a discrete-time NCS representation.…”

Real-time control systems: feedback, scheduling and robustness

“…The authors have proposed (among others, e.g. (Hetel, Daafouz, and Iung (2006))) Linear Parameter Varying (LPV) models of digital control systems with varying sampling, under the assumption that the system representation is affine with respect to the sampling interval (Robert et al (2006)). …”