Global stability results for systems under sampled‐data control

Abstract

In this work sufficient conditions expressed by means of single and vector Lyapunov functions of Uniform Input-to-Output Stability (UIOS) and Uniform Input-to-State Stability (UISS) are given for finite-dimensional systems under feedback control with zero order hold.

Stabilization of nonlinear sampled-data systems and economic model predictive control application

“…Using Eq. 9 and since a ≤ τ 1 ≤ ∆ * , a bound on the difference between x(t) and x(0) is obtained: (14) for all t ∈ [0, a]. Applying the Gronwall-Bellman lemma to Eq.…”

“…For guaranteed performance improvement with the proposed LEMPC scheme, both layers are formulated with explicit performance-based constraints computed from an auxiliary Lyapunov-based model predictive control (LMPC) problem solution formulated with a quadratic cost. Typically, when a sample-and-hold controller, such as LMPC, is applied to a continuous-time system, the resulting closed-loop system achieves practical stability (e.g., [14], [18]). However, when considering the asymptotic average closed-loop performance under LMPC (i.e., infinite-time performance), asymptotic stabilization of the closed-loop system under LMPC is needed.…”

Global sampled-data output feedback stabilisation for a class of nonlinear systems with unknown output function

“…One approach is to design a discrete-time controller based on the discrete-time approximation of the nonlinear system (Nesic, Teel, & Kokotovic, 1999;Ustunturka & Kocaoglana, 2013) which can only guarantee local or semi-global stabilization owing to the existence of approximation errors. The other approach is to design a sampled-data controller based on the emulation method by discretizing continuous-time controllers (Dabroom & Khalil, 2001;Karafyllis & Kravaris, 2009; A c c e p t e d M a n u s c r i p t ugust 7, 2015 International Journal of Control ijcR1 Teel, & Carnevale, 2009;Owen, Zheng, & Billings, 1990;Qian & Du, 2012). The issue in the emulation method is the choice of the sampling period T .…”

“…A sampled-data controller is constructed based on the output feedback domination approach to globally stabilize the nonlinear systems in (Qian & Du, 2012). Sufficient conditions for global stability under sampled-data control with zero order hold are expressed by means of single and vector Lyapunov functions in (Karafyllis & Kravaris, 2009). The work (Du et al, 2013) investigates the problem of designing a sampled-data output feedback controller to globally stabilize a class of upper-triangular systems with delay in the input.…”

Global sampled-data stabilization of a class of nonlinear systems

“…Nonlinear systems is different from linear systems which can obtain the exact discretized model to design controller. Recently, some approaches are introduced to solve the problem, for example, discrete-time design [10], the emulation method [11,12,13,14,15,16,17], and continuous-discrete design [16,17,18,19,20]. Global stabilization problem of a class of inherently nonlinear systems with uncertain parameters is studied in [20].…”