Robust $$H_\infty $$ H ∞ Repetitive Control for a Class of Linear Stochastic Switched Systems with Time Delay

Abstract

This paper investigates the problem of robust H ∞ repetitive control for a class of linear stochastic switched systems with time delay. Based on the lifting technique, a continuous-discrete stochastic 2D (two-dimensional) delayed model is firstly proposed to describe the control and learning actions of the repetitive control system. Then a sufficient condition for the asymptotical stability with H ∞ performance of the 2D model is derived by choosing an appropriate common Lyapunov functional. The feedback controller gains are then obtained by solving a set of linear matrix inequalities. One example is given to illustrate the effectiveness of the proposed method.

State-Estimator-Based Asynchronous Repetitive Control of Discrete-Time Markovian Switching Systems

“…Based on the numerical simulations results, the asynchronous repetitive control method proposed in this paper has the following advantages over the methods provided in [32][33][34][35][36][37][38][39]: (1) the proposed method does not require the controller or estimator to switch synchronously with the plant; (2) the proposed asynchronous repetitive control method is broader and inclusive in the sense that a variety of more restrictive cases can be obtained from it. For example, when N � M and μ ip � 1 for p � i, i.e., μ � I, the asynchronous repetitive control method reduces to the synchronous mode-dependent case.…”

“…Since the control tasks in many applications that can be modeled by such systems are often repetitive, increased use of repetitive control formulations can be found in many applications, disk drive systems [28], rotating machinery [29], micro-/nanomanipulation applications [30], and power electronics systems [31]; repetitive control strategies use error measurements from the previous period to reduce subsequent steady-state tracking errors for periodic exogenous input signals. ere is a rich body of literature related to repetitive control design techniques [32][33][34][35][36][37][38][39][40]. Most repetitive control designs in the literature are developed for deterministic systems, whereas designs for switched stochastic dynamical systems are sparse.…”

Repetitive control design for vehicle lateral dynamics with state‐delay

“…If the control process is partitioned into pieces arranged in a order with their length representing the repetitive time, then we can observe two dynamic behaviours in the modified repetitive control system: control action (continuous) and learning action (discrete). Describing the control action with a continuous differential equation and learning with a discrete difference equation yields a continuous‐discrete two‐dimensional hybrid model [21, 22]. A hybridised two‐dimensional exposes the essence of modified repetitive control illustrates a better control performance when comparing to traditional one‐dimensional continuous model.…”

Tracking and disturbance attenuation control for stochastic switched systems with input delay

“…For enhancing the tracking performance for control systems, repetitive‐control design is introduced in [9, 10], which has a self‐learning potential and periodic signal generator. In addition, repetitive control is utilised for the analysis of qualitative behaviours of the dynamical systems subject to periodic disturbances.…”