Induced norms for sampled-data systems

✍ Scribed by N. Sivashankar; Pramod P. Khargonekar

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 465 KB
• Volume: 28
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(92)90072-n

✦ Synopsis

In this paper, we consider a general linear interconnection of a continuous-time plant and a discretetime controller via sample and hold devices. When the closed loop sampled-data feedback system is internally stable, bounded inputs produce bounded outputs. We present some explicit formulae for the induced norm of the closed loop system with ~ (i.e. peak value) and ~1 (i.e. integral absolute) norms on the input and output signals.

interfaced with each other using analog-to-digital (A/D) and digital-to-analog (D/A) converters. We will omit in this paper the fact that the A/D converter also involves quantization in magnitude of signals and are thus really nonlinear operators. We will treat them as ideal sampler and ideal hold devices. It is of interest to extend the notion of system norms for sampled-data systems.

Recently, many papers have appeared that deal with and ~ norms for sampled-data systems. Bamieh and Pearson (1992), Ba~ar (1991), Chen and Francis (1990), Kabamba and Hara (1990), Sun et al. (1991), Tadmor (1991) and Toivonen (1992) have considered ~ optimal control problems while Bamieh and Pearson (1991), Chen and *