Finite-frequency model order reduction of discrete-time linear time-delayed systems

Abstract

This paper discusses model order reduction of discrete-time linear time-delayed systems over limited frequency interval. Firstly, a finite-frequency index is introduced to characterize the desired approximation performance over the pre-specified frequency interval. By exploiting the finite-frequency analysis results for linear delay systems, sufficient criterions for guaranteeing stability of the reduced-order model and optimizing the finite-frequency approximation error are derived with the aid of matrix inequality techniques. The finitefrequency model order reduction problem then is converted to a LMI-based optimization problem, which can be solved easily. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.

Model reduction for discrete-time switched linear time-delayed systems with finite-frequency specifications

“…Zhao et al (2014) used the average dwell time (ADT) method to design the estimator of the discrete-time switched positive system. However, there are few studies on model reduction of switched linear systems, such as Du et al (2016), Maraoui et al (2017) and Shi et al (2013).…”

Fault‐Tolerant Finite Frequency H∞ Control for Uncertain Mechanical System with Input Delay and Constraint

“…In this regard, we suppose that if H ∞ performance index is only designed for the certain frequency region covering the leading vibration modes in the design process of H ∞ controller, which implies the limited energies of actuator are all focused on this frequency range, a less conservative controller and better disturbance rejection effect, compared with entire frequency approach, could be achieved. During the past decade, the problem of finite frequency control has been studied in H ∞ control and filtering , model reduction , and fault detection . However, few published articles involve the reliable finite frequency control for uncertain mechanical system with input delay and constraint.…”

Generalized gramian based frequency interval model reduction for unstable systems

“…Many problems which involve the computation of gramians are inherently frequency dependent [5]- [9]. Shaker had applied frequency limited controllability and observability gramians for input-output interactions for control configuration selection and also for the measurement of control reconfigurability in the context of fault tolerant control systems [10], [11].…”