Input-output Approach and Scaled Small Gain Theorem Analysis to Sampled-data Systems with Time-varying Delay
- PDF / 433,421 Bytes
- 9 Pages / 594.77 x 793.026 pts Page_size
- 65 Downloads / 163 Views
ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Input-output Approach and Scaled Small Gain Theorem Analysis to Sampled-data Systems with Time-varying Delay Ouarda Lamrabet*, El Houssaine Tissir, Nabil El Fezazi, and Fatima El Haoussi Abstract: This article presents some novel results on sampled-data H∞ control for a class of linear systems. The proposed system is affected by time-varying delay and external disturbance. The main goal of this paper is to transform the original system into an equivalent two interconnected subsystems through the combination of input-output approach and scaled small gain (SSG) theorem. Then, the three term approximation method is adopted to approximate the time-varying delay. By incorporating Lyapunov-Krasovskii functional and wirtinger integral inequality, a new set of sufficient conditions is obtained in terms of linear matrix inequalities (LMIs), which guarantee the stability of the closed loop system, and a H∞ norm bound performances. Finally, the applicability of the developed control design technique and its less conservativeness over other existing ones are proven by means of simulation examples. Keywords: H∞ control, sampled-data control, scaled small gain theorem, time-varying delay.
1.
INTRODUCTION
Since sampled-data control has a wide range of successful applications in a lot of fields, it has received significant attention from the control community. In this connection, numerous results on the analysis and design of sampled-data control problem for dynamical systems have been developed [1–4]. Among a variety of methodologies to deal with sampled-data systems, input delay approach is widely used, which allows modelling the sampled-data system as a continuous-time system with a delayed control input [5, 6]. Time delay is a common phenomenon occurring in all dynamical systems such as network systems [7, 8], singular systems [9] and so on. It is the major cause of performance loss, divergences and instability. Over the last halfcentury, such systems have attracted many attention, see [10–12]. Additionally, in the literature, several approaches allowing the analysis and control of a time-delay system have been established. For example, the augmented Lyapunov-Krasovskii functional method [13], Wirtinger inequality approach [14, 15] and Free-matrix-based Integral Inequality [16, 17]. It has also been shown that the input-output (IO) approach [18] is an effective technique to reduce the conservatism of the results, where the original system is transformed into two interconnected subsystems. Then, by using the small-gain theorem [19], we can
demonstrate that the stability condition can considerably be improved. The basic idea of this method is to establish a suitable approximation for the time-varying delay, such that the approximation error is as small as possible. In the literature, several results can be found concerning the IO approach. In [20] the delayed state x(t − d(t) is approximated by its average value 12 (x(t − d1 ) + x(t − d1 )) (twoterms approximation
Data Loading...
