Stability analysis and design of nonlinear sampled‐data systems under aperiodic samplings

Abstract

In this paper, the problem of exponential stability analysis and the design of sampled-data nonlinear systems have been studied using a polytopic linear parameter-varying approach. By means of modeling a new double-layer polytopic formulation for nonlinear sampled-data systems, a modified form of piecewise continuous Lyapunov-Krasovskii functional is proposed. This approach provides less conservative robust exponential stability conditions by using Wirtinger's inequality in terms of linear matrix inequalities. The distances between the real continuous parameters of the plant and the measured parameters of the controller are modeled by convex sets, and the analysis/design conditions are given at the vertices of some hyper-rectangles. In order to get tractable linear matrix inequality conditions for the stabilization problem, we performed relaxation by introducing a slack variable matrix. Under the new stability criteria, an approach is introduced to synthesize a sampled-data polytopic linear parameter-varying controller considering some constraints on the location of the closed-loop poles in the presence of uncertainties on the varying parameters. It is shown that the proposed controller guarantees the exponential stability of the closed-loop system for aperiodic sampling periods smaller than a known value, ie, maximum allowable sampling period. Finally, the effectiveness of the proposed approach is verified and compared with some state-of-the-art existing approaches through numerical simulations.

Wind turbines power regulation using a low-complexity linear parameter varying-model predictive control approach

“…The problem of the analytical calculation of the maximum allowable sampling period has been recently studied in the context of sampled-data control systems (see e.g. Hooshmandi et al (2018a,b)). A general rule is to choose the sampling frequency greater than (at least two times) the frequency of the fastest mode in the continuous-time system.…”

Admissibility Analysis of a Sampled‐Data Singular System Based on the Input Delay Approach

“…e third one is the input delay method (see [23]), and the system is transformed into a continuous timevarying delay system, and then the stability analysis can be accomplished using the method of time-delay system. Besides, the input delay approach can deal with the uncertainty of system parameters, and it has been widely used in the sampled-data system (see [24,25]) and practical engineering field such as autonomous airship, high-speed train, and dynamic positioning ship (see [26][27][28]). In [24], based on the polytopic linear parameter-varying method, the issue of the sampled-data control is discussed for a nonlinear system.…”

“…Besides, the input delay approach can deal with the uncertainty of system parameters, and it has been widely used in the sampled-data system (see [24,25]) and practical engineering field such as autonomous airship, high-speed train, and dynamic positioning ship (see [26][27][28]). In [24], based on the polytopic linear parameter-varying method, the issue of the sampled-data control is discussed for a nonlinear system. And Wirtinger's inequality is used to obtain less conservative exponential stability condition.…”

Robust global controller design for discrete‐time descriptor systems with multiple time‐varying delays

“…Causality, regulation, and stabilization are a vital topics in the study of discrete‐time descriptor systems . Time delays are quite common in practical applications and have an impact on system's causality, regulation, and stability . Consequently, much consideration has been given to the stabilization and tracking control of these systems .…”