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Technical Brief

# Two-Stage Feedback Control Design for a Class of Linear Discrete-Time Systems With Slow and Fast Modes

[+] Author and Article Information

Mem. ASME
Department of Mechanical Engineering,
Villanova University,
800 E. Lancaster Avenue,
Villanova, PA 19085
e-mail: verica.gajic@villanova.edu

$O(ɛi)$ is defined as $O(ɛi), where $c$ is a bounded constant and $i$ is a real number.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 23, 2014; final manuscript received February 14, 2015; published online April 21, 2015. Assoc. Editor: M. Porfiri.

J. Dyn. Sys., Meas., Control 137(8), 084502 (Aug 01, 2015) (6 pages) Paper No: DS-14-1347; doi: 10.1115/1.4030088 History: Received August 23, 2014; Revised February 14, 2015; Online April 21, 2015

## Abstract

In this paper, we first review the new algorithm for the two-stage feedback controller design of linear discrete-time systems, and then provide conditions for its applicability. The design algorithm is specialized and simplified for a class of linear systems with slow and fast modes (multitime scale systems or singularly perturbed systems). The proposed design significantly reduces computational full-state feedback design requirements and provides independent and accurate feedback controller design techniques in slow and fast time scales. We present also conditions needed for applicability of the proposed two-stage design in two time scales. The power of the two-stage design lies in the fact that different types of controllers can be designed for different subsystems using the corresponding feedback gains obtained by performing calculations only with the subsystem (reduced-order) matrices.

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