Asymptotic Stabilization of Continuous-Time Linear Systems with Input and State Quantizations

Sung Wook Yun,Jin Young Park,Sung Hyun Kim

doi:10.1155/2014/947164

Abstract

This paper discusses the asymptotic stabilization problem of linear systems with input and state quantizations. In order to achieve asymptotic stabilization of such systems, we propose a state-feedback controller comprising two control parts: the main part is used to determine the fundamental characteristics of the system associated with the cost, and the additional part is employed to eliminate the effects of input and state quanizations. In particular, in order to implement the additional part, we introduce a quantizer with a region-decision making process (RDMP) for a certain linear switching surface. The simulation results show the effectiveness of the proposed controller.

Highlights

In the field of control systems, quantized feedback systems have attracted considerable attention because quantization errors in actuators and sensors have adverse effects on the general performance of systems; for example, they can affect the transient response, steady-state response, or stability
Like the controllers in [15,16,17], the proposed controller consists of main and additional control parts. The former is responsible for determining the fundamental characteristics of the system associated with the cost and the latter is responsible for simultaneously eliminating the effects of input and state quantizations
In order to implement the latter part, we introduce a quantizer with a region-decision making process (RDMP), where the RDMP plays the role of determining where the state is located with respect to a certain linear switching surface

Summary

Introduction

In the field of control systems, quantized feedback systems have attracted considerable attention because quantization errors in actuators and sensors have adverse effects on the general performance of systems; for example, they can affect the transient response, steady-state response, or stability. The goal of this paper is to develop a control policy without the aforementioned assumptions in order to achieve asymptotic stabilization of systems using combined quantization. Like the controllers in [15,16,17], the proposed controller consists of main and additional control parts The former is responsible for determining the fundamental characteristics of the system associated with the cost and the latter is responsible for simultaneously eliminating the effects of input and state quantizations. The main contribution of this paper is the design of a novel RDMP quantizer-based state-feedback controller that achieves asymptotic stability for quantized feedback systems. The merit of the proposed controller is that asymptotic stability can be achieved regardless of the assumptions such as adjustable sensitivity and an infinite number of quantization levels. Ei is a unit vector with the ith nonzero entry; that is, ei ≜ [0 ⋅ ⋅ ⋅ ⏟⏟⏟1⏟⏟ ⋅ ⋅ ⋅ 0]T

System Description

Main Results

Simulation Results

Conclusion