Class Of Uncertain Delay Systems Research Articles

A linear matrix inequality approach for robust control of systems with delayed states

This paper addresses the robust stabilization problem for uncertain systems with delayed states. The parameter uncertainties are unknown but norm-bounded and the delay is time-varying. In this study, a linear matrix inequality (LMI) approach for robust stability analysis for the nominal unforced system and a method for robust stabilization for a class of uncertain delay systems via linear memoryless state feedback control are presented. The results depend on the size of the delay and are given in terms of linear matrix inequalities.

A stabilizing control for a class of uncertain delay systems with limited measurable state variables

The previously obtained stabilizing control for the delayed linear systemsis developed to the systems which can provide only two state variablesincluding no delays, whereas whole state variables were needed so far. Thesetwo state variables are the ones specified in relation to the uncertainparameters. The obtained condition is equivalent to the previous one.However, to obtain the same size of attracting region controls with largergains are needed comparative to the previous result.

Robust stability for time-delay systems: the edge theorem and graphical tests

The robust stability problem is discussed for a class of uncertain delay systems where the characteristic equations involve a polytope P of quasi-polynomials (i.e. polynomials in one complex variable and exponential powers of the variable). Given a set D in the complex plane, the goal is to find a constructive technique to verify whether all roots of every quasi-polynomial in P belong to D (that is, to verify the D-stability of P). First it is demonstrated by counterexample that Kharitonov's theorem does not hold for general delay systems. Next it is shown that under a mild assumption on the set D a polytope of quasi-polynomials is D-stable if and only if the edges of the polytope are D-stable. This extends the edge theorem for the D-stability of a polytope of polynomials. The third result gives a constructive graphical test for checking the D-stability of a polytope of quasi-polynomials which is especially simple when the set D is the open left-half plane. An application is given to demonstrate the power of the results. >