5 research outputs found
Stability Analysis of Integral Delay Systems with Multiple Delays
This note is concerned with stability analysis of integral delay systems with
multiple delays. To study this problem, the well-known Jensen inequality is
generalized to the case of multiple terms by introducing an individual slack
weighting matrix for each term, which can be optimized to reduce the
conservatism. With the help of the multiple Jensen inequalities and by
developing a novel linearizing technique, two novel Lyapunov functional based
approaches are established to obtain sufficient stability conditions expressed
by linear matrix inequalities (LMIs). It is shown that these new conditions are
always less conservative than the existing ones. Moreover, by the positive
operator theory, a single LMI based condition and a spectral radius based
condition are obtained based on an existing sufficient stability condition
expressed by coupled LMIs. A numerical example illustrates the effectiveness of
the proposed approaches.Comment: 14 page
Backstepping and Sequential Predictors for Control Systems
We provide new methods in mathematical control theory for two significant classes of control systems with time delays, based on backstepping and sequential prediction. Our bounded backstepping results ensure global asymptotic stability for partially linear systems with an arbitrarily large number of integrators. We also build sequential predictors for time-varying linear systems with time-varying delays in the control, sampling in the control, and time-varying measurement delays. Our bounded backstepping results are novel because of their use of converging-input-converging-state conditions, which make it possible to solve feedback stabilization problems under input delays and under boundedness conditions on the feedback control. Our sequential predictors work is novel in its ability to cover time-varying measurement delays and sampling which were beyond the scope of existing sequential predictor methods for time-varying linear systems, and in the fact that the feedback controls that we obtain from our sequential predictors do not contain any distributed terms