3 Sampled-data Control of Nonlinear Systems

Input‐to‐state stability, numerical dynamics and sampled‐data control

“…These results are similar in spirit to [24,23] (for an introduction to the subject see [18]), with the difference that here we derive necessary and sufficient conditions instead of merely sufficient conditions.…”

“…When proceeding this way we face the problem that the discrete time system Φ u h induced by (7.3) is hardly ever known exactly, because it is the solution of a nonlinear ordinary differential equation. Therefore, typically one has to design the feedback controller for a family of approximations Φ u k , k ∈ N, to Φ u h , see, e.g., [4,5,9,10,11,12,18,21,25,27,26] for examples of such design methods. Since a feedback law constructed on basis of an approximation Φ u k will depend on k, we need to consider sequences of feedback laws u k in the following definition of the approximating systems:…”

“…Of course, the regularity of the maps u k strongly depends on the sampled data feedback design method employed. While for series based (re-)design methods as presented, e.g., in [11,21,25] or for the Euler backstepping method [27,18] the Lipschitz property can be expected or even rigorously proved, optimal control based design methods as in [5,9,10,12,26] typically yield discontinuous feedback laws u k , for which convergence (7.6) cannot be expected in general.…”

Observers and output feedback stabilising controllers for nonlinear strict-feedback systems with sampled observation

“…For continuous-time strict-feedback systems, the stability analysis and the design of stabilising state feedback laws such as a backstepping and a feedback linearisation have been widely considered (for details see Khalil (2002), Kristic, Kanellakopoulos, and Kokotovic (1995), and references therein). Recently, they have been extended to (parameterised) discretetime and sampled-data strict-feedback systems (Nešić & Loría, 2004;Nešić & Teel, 2006;Postoyan, AhmedAli, & Lamnabhi-Lagarrigue, 2009) by using the framework to design sampled-data control systems on the basis of approximate discrete-time models (Laila, Nešić, & Astolfi, 2005;Nesic, Teel, & Kokotovic, 1999;Nešić, Teel, & Sontag, 1999) where a sampled-data system is a continuous-time system with sampled observation and control input realised through a zero-order hold. In the proposed framework, other stability analysis and several design methods of state feedback stabilising laws have been also given for the general sampled-data system (Monaco, Normand-Cyrot, & Tiefensee, 2011;Nešić & Grune, 2005Nešić & Laila, 2002).…”

Decentralized Integral-Based Event-Triggered Stabilization for Linear Plant with Actuator Saturation and Output Feedback

“…In this control strategy, the control task execution is decided by an event instead of a certain fixed period of time. The latter is known as periodic sampling or time-triggered control [1]. The event is generated by the designed event condition, which is a state-related criterion.…”