Delay‐dependent conditions for finite time stability of linear time‐varying systems with delay

This paper addresses the regional stability problem for impulsive switched nonlinear systems (ISNSs) whose subsystems have more than one equilibrium point, that is, multiple equilibrium points (MEPs) coexist. Meanwhile, we derive analytical results and sufficient conditions about the regional stability. Through investigating the dynamical behavior of ISNSs with MEPs, the multiple Lyapunov functions (MLFs) method is established for the regional stability. It is shown that main results obtained in this paper not only guarantee the regional stability of ISNSs with MEPs under arbitrary switching signals but also provide a new method to determine the corresponding stable regions for the regional stability. Numerical simulations are given to illustrate and verify advantages of our proposed results.

Section: Resultsmentioning

confidence: 99%

“…On the other hand, significant progress has been made in the theory of regional stability [22‐27]. The problem of regional stability analysis of two‐dimensional nonlinear polynomial systems represented by the Fornasini–Marchesini second state‐space model was addressed in Osowsky et al [22].…”

Section: Introductionmentioning

confidence: 99%

Regional stability analysis of impulsive switched nonlinear systems with multiple equilibrium points

Wang

Feng

2020

“…Remark 1. Due to a large number of research results on the stability of time-delay systems [29][30][31], we only need to choose a commonly used method to verify the system stability. Lemma 1 often used for stability analysis of general time-delay systems due to its simplicity.…”

Section: Stability Analysismentioning

confidence: 99%

Observer‐based trajectory control for directional drilling process

Cai

Lai

et al. 2021

This paper is concerned with observer-based trajectory control of directional drilling system with rotary steering devices. Since the trajectory orientation cannot be measured directly, most of the existing results implicitly assume that the trajectory orientation is equal to the measurement of orientation of the bottom hole assembly (BHA) or the drill bit, which would bring in certain control errors in practice. To avoid such control errors, in this paper, a trajectory control approach is established, which includes a state observer to estimate the trajectory orientation based on the measurement of the BHA orientation. Firstly, the relationship between the trajectory orientation and the BHA orientation is analyzed, and a trajectory evolution model is introduced according to the analysis. Secondly, based on this trajectory evolution model, a variable transformation technique is applied such that a trajectory tracking control problem is formulated. Thirdly, a feedback control strategy is devised based on the estimation of the trajectory orientation for trajectory tracking. Fourthly, stability analysis of the closed-loop system is discussed, and the design of the controller and state observer is done.

“…However, with the increasing demands of modern control for control performance, time-invariant systems may fail to be effective, and time-varying characteristics of systems must be taken into consideration. Recently, time-varying systems have attracted significant attention, and many contributions have been achieved, especially for linear time-varying systems (LTVSs) [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Robust predictive iterative learning control for linear time‐varying systems

Liang

Zou

Cai

2021

A novel control technique is proposed by combining iterative learning control (ILC) with model predictive control (MPC) for a trajectory tracking problem of linear time-varying systems (LTVSs) in this paper. By introducing prediction mechanism along both of the iteration and time directions instead of only one direction, the control law is successively updated along two directions by learning from the predictive and compensatory information. The new control law can improve convergence speed and effectively suppress the uncertainties in initial states, external disturbances, and model mismatches. The convergence conditions are rigorously derived and analyzed as well. An example is given to illustrate the effectiveness of the obtained results.