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This note provides sufficient robust stability conditions for continuous time polytopic systems. They are obtained from the Frobenins--Perron Theorem applied to the time derivative of a linear parameter dependent Lyapunov function and are expressed in terms of linear matrix inequalities (LMI). They contain as special cases, various sufficient stability conditions available in the literature to date. As a natural generalization, the determination of a guaranteed [H.sub.2] cost is addressed. A new gain parametrization is introduced in order to make possible the state feedback robust control synthesis using parameter dependent Lyapunov functions through linear matrix inequalities. Numerical examples are included for illustration. Index Terms--Linear matrix inequalities (LMIs), linear systems, robust control design, robust stability and performance.

The aim of this paper is to present new results on ℋ∞ control synthesis for time-delay linear systems. We extend the use of a finite order LTI system, called comparison system to ℋ∞ analysis and design. Differently from what can be viewed as a common feature of other control design methods available in the literature to date, the one presented here treats time-delay systems control design with classical numeric routines based on Riccati equations arisen from ℋ∞ theory. The proposed algorithm is simple, efficient and easy to implement. Some examples illustrating state and output feedback design are solved and discussed in order to put in evidence the most relevant characteristic of the theoretical results. Moreover, a practical application involving a 3-DOF networked control system is presented. [ABSTRACT FROM AUTHOR]

This paper introduces a new procedure for \cal H\infty filter design of time-delay linear systems. A finite-order LTI system, called comparison system, is defined in such a way that its \cal H\infty norm is proven to be strongly related to the one of the time-delay system. Differently from what can be viewed as a common feature of filter design methods available in the literature to date, the one presented here treats the filtering design of time-delay systems with classical numerical routines based on Riccati equation and \cal H\infty theory of LTI systems. The proposed algorithm is simple, efficient and easy to implement. Illustrative examples are solved and discussed in order to put in evidence the most relevant properties of the theoretical results. Furthermore, a practical application is presented. [ABSTRACT FROM AUTHOR]