Analysis and Synthesis of State-Feedback Controllers With Timing Jitter

Abstract

Abstract-We consider a continuous-time linear system with sampled constant linear state-feedback control and a convex quadratic performance measure. The sample times, however, are subject to variation within some known interval. We use linear matrix inequality (LMI) methods to derive a Lyapunov function that establishes an upper bound on performance degradation due to the timing jitter. The same Lyapunov function can be used in a heuristic for finding a bad timing jitter sequence, which gives a lower bound on the possible performance degradation. Numerical experiments show that these two bounds are often close, which means that our bound is tight. We show how LMI methods can be used to synthesize a constant statefeedback controller that minimizes the performance bound, for a given level of timing jitter.

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.…”

A Delay-Dependent Dual-Rate PID Controller Over an Ethernet Network

“…Several alternatives to overcome such limitation can be considered in the framework of uncertain systems. In [24], a grid generation algorithm is provided to remove the above issue; in [30], a Lipschitz-like condition is used; some convex bounds of the relevant set of matrices are suggested in [25] (via Taylor expansions) and [26] (based on the exponential of the real Jordan form). In [29], multiple loops sharing a network are considered; depending on which node has the network access, a different model is obtained; the networked control system is considered to be an uncertain discrete switched system for LMI analysis.…”

Design of an Embedded Control System Laboratory Experiment

“…Furthermore, it is known that, in multitasking real-time control systems, jitters, i.e., timing interferences on control tasks due to the concurrent execution of other tasks, deteriorate the control loop performance [41]. The objective of this implementation is to observe these degrading effects and implement corrective actions, e.g., [42]- [44].…”

“…Another solution could be to enforce synchronized executions at the kernel level, using the EDF tick counter. Moreover, since different solutions to the jitter problem, such as that in [42] or [43], could have also been applied, students that are more confident or interested in specific fields can select the solution that better meets their preferences.…”