Passive Control of Sampling System - Intelligent Computing for Sustainable Energy and Environment - page 139

Passive Control of Sampling System
Wenyuan Li
Department of Computer, Harbin Financial Institute
Harbin, 150080, China
wxl [e-mail]
Abstract. The passive control problem of a class of uncertain state-
delay sampling system is discussed. Applying Lyapunov method, and
combining the properties of matrix inequality, the sucient condition
of passive stability is given, and passive controller is designed. Finally,
a numerical example illustrates the effectiveness and availability for the
design.
Keywords: Uncertain state-delay system, Sampling system, Passive
control, Linear Matrix Inequality.
1 Introduction
Researches on passive stability of the sampling system were very active in the
past decades[1, 2]. Several approaches have been proposed to solve passive stabil-
ity of the sampling system. Literature [3] discusses passive stability of sampled
system using Riccati equation approach. Literature [4] discusses passive sta-
bility of sampled system for a class of non-structural perturation models using
time-domain approach. Literature addresses passive control of a class of sampled
systems with structured uncertainty using LMI approach. Literature addresses
passive state feedback control of uncertain sampled system with pole constrain.
But it isn't perfect, they only consider uncertainty of the system parameters
without taking into account of uncertainty of controller gain. when there is per-
turbation in controller parameters ( for example, which often occurs that the
system initially runs, the controller finely tunes and the controller gain parame-
ters change when controller performance deterioration ) , the traditional passive
control methods shows a highly fragile [5-8], which results in that closed-loop
system performance decreased and stability damage. Therefore, we must take
into account uncertainties in the controller to guarantee the stable and high-
performance operation of the system.
Based on this, this article considers passive control problem of the uncertain
time-delay a sampled system with perturbations of controller gain, in the con-
troller gain of two forms with the addition and multiplication, we discusses with
the design method of the controller gain and gives passive controller's existence
sucient condition of the uncertain time-delay sampled system , which depends
on the LMIs feasible solution, and is verified by simulation examples.