Controller Synthesis on Non-uniform and Uncertain Discrete–Time Domains

Abstract

Abstract. The problem of synthesizing feedback controllers that perform sensing and actuation actions on non-uniform and uncertain discrete time domains is considered. This class of problems is relevant to many application domains. For instance, in engine control a heterogenous and, to some extent, uncertain event-driven time domain is due to the behavior of the 4-stroke internal combustion engine, with which the controller has to synchronize to operate properly. Similar problems arise also in standard discrete-time control systems when considering the behavior of the system with controller implementation and communication effects. The design problem is formalized in a hybrid system framework; synthesis and verification methods, based on robust stability and robust performance results, are presented. The effectiveness of the proposed methods is demonstrated in an engine control application.

Constructing a bimodal switched Lyapunov function for non-uniformly sampled-data feedback systems

“…Then the main difficulty to be solved is the fact that the discrete-time system is time-varying and uncertain. Improving the approximation by gridding in earlier studies [1], [21], [28], the recent studies take the robustness into account to guarantee the stability. In particular, (i) a robust control approach based on a linear fractional transformation (LFT) uncertainty modeling [6], [8], [24], (ii) a robust control approach based on a polytopic uncertainty modeling [1], [2], [11], [12], and (iii) a robust linear matrix inequality (LMI) approach [19], [20] have been proposed.…”

“…Improving the approximation by gridding in earlier studies [1], [21], [28], the recent studies take the robustness into account to guarantee the stability. In particular, (i) a robust control approach based on a linear fractional transformation (LFT) uncertainty modeling [6], [8], [24], (ii) a robust control approach based on a polytopic uncertainty modeling [1], [2], [11], [12], and (iii) a robust linear matrix inequality (LMI) approach [19], [20] have been proposed. We note that numerical experiences in the references suggest that these discrete-time approaches are less conservative than other approaches constructing continuous-time Lyapunov functions in, e.g., [4], [5], [7], [14]- [18], [23], [25]- [27].…”

“…Motivated by networked control systems with packet loss (See, e.g., [10]) and embedded control systems with incomplete real-time property (See, e.g., [13]), analysis and design problems for sampled-data systems with uncertainly timevarying sampling intervals have been studied in these days [1], [2], [4]- [9], [11], [12], [14]- [28]. It is obvious that the problems are much harder than those for the standard periodic sampling case, and that robustness plays a crucial role in the study.…”

LMI control design for a class of exponential uncertain systems with application to network controlled switched systems

“…forêt de la Haye, 54516, Vandoevre-Lès-Nancy, Cedex, France. Corresponding author: jamal.daafouz@ensem.inpl-nancy.fr Work (partially) done in the framework of the HYCON Network of Excellence, contract number FP6-IST-511368 Consider a continuous time system such as (1) where the command is affected by unknown time-varying networked induced delays τ (k) :…”

“…In the literature, the problem is treated by assuming that the uncertain delay, can be estimated [13], or that it is governed by an underlying Markov chain [10]. Other authors [1] treat the uncertain exponential terms as bounded uncertainties but the obtained results may be too conservative. In our opinion, no efficient solution has been given yet.…”