Gain-scheduled L-one control for linear parameter-varying systems with parameter-dependent delays

Abstract

This paper deals with the problem of gain-scheduled L-one control for linear parameter-varying (LPV) systems with parameter-dependent delays. The attention is focused on the design of a gain-scheduled L-one controller that guarantees being an asymptotically stable closed-loop system and satisfying peak-to-peak performance constraints for LPV systems with respect to all amplitude-bounded input signals. In particular, concentrating on the delay-dependent case, we utilize parameter-dependent Lyapunov functions (PDLF) to establish peak-to-peak performance criteria for the first time where there exists a coupling between a Lyapunov function matrix and system matrices. By introducing a slack matrix, the decoupling for the parameter-dependent time-delay LPV system is realized. In this way, the sufficient conditions for the existence of a gain-scheduled L-one controller are proposed in terms of the Lyapunov stability theory and the linear matrix inequality (LMI) method. Based on approximate basis function and the gridding technique, the corresponding controller design is cast into a feasible solution problem of the finite parameter linear matrix inequalities. A numerical example is given to show the effectiveness of the proposed approach.

L1 impedance control for bilateral teleoperation containing model uncertainty

“…Recalling τ · ≤ d ~ , the theorem can be proved in a similar manner to Theorem 2 of Li and Liang (2011) by putting matrix Z therein equal to zero and eliminating its corresponding rows and/or columns in each matrix.■…”

“…L 1 filtering methods for systems with time delays have also been investigated by Li et al (2008, 2011). Designing controller for delayed systems is proposed by Li and Liang (2011), Maiti et al (2021), and Yungang et al (2000) by means of optimal L 1 theory, and by Nguyen and Dankowicz (2017) by making use of L 1 adaptive control.…”

Position synchronization for an uncertain teleoperation system with time delays using L1 theory

“…( 13) is asymptotically stable that guarantees the L 1 performance criterion (i.e., with the noise attenuation level of ), if there exist a scalar > 0 and matrices P () > 0, Q() > 0, R() > 0, and W () with appropriate dimensions satisfying Inequalities ( 18), ( 19) and (35): Proof. The proof could be easily concluded from Theorem 2 of [22], putting matrix Z therein equal to zero and omitting its respective rows and/or columns in each matrix. Finally, the third part of the L 1 controller synthesis is as follows.…”

“…For example, in [20], a small-gain theorem was developed for timedelayed systems based on L 1 theory, or in [21], L 1 ltering methods were proposed for systems with time delay. In addition, in [22], the design of a controller for systems with latency based on the optimal L 1 theory for linear parameter-varying systems was investigated. In [23], the very case for air heater systems was studied.…”

Robustness Convergence for Iterative Learning Tracking Control Applied to Repetitfs Systems

“…For a prescribed scalar, γ, J(γ) can be transformed as the performance index defined for the system. This 1D equivalent model was developed in previous research [22,23], and here it is only necessary to give the final construction. Here, " x kþ1 ðtÞ represents the input state vector, " y kþ1 ðtÞ is the output vector, w k +1 (t) ∈ ℝ q is the exogenous input that belongsl 2 {[0, ∞), [0, ∞)}, and z k+1 (t) is the controlled output.…”