Global and Semi-Global Stabilization of Linear Systems With Multiple Delays and Saturations in the Input

Abstract

This paper studies stabilization problems for linear systems with multiple delays in the input. Two types of delays are considered. The first type of delays is constant delays, which can be arbitrarily large, while the second type is time-varying with an arbitrarily large bound. With the first type of delays, under the condition that the open loop system is absolutely controllable with all its eigenvalues on the imaginary axis, (globally) stabilizing state and output feedback laws are constructed based on the solution to a family of parametric Riccati equations, which can be obtained explicitly through the solution of a parametric linear matrix equation. With the second type of delays, under the condition that the open-loop system is absolutely controllable with all its eigenvalues on the imaginary axis being zero, (global) state and output feedback laws are explicitly constructed based on the solution to a similar family of parametric Riccati equations. When the input is also subject to magnitude saturation, it is shown that semiglobal stabilization, instead of global stabilization, can still be achieved. Numerical examples illustrate the effectiveness of the proposed approach.

Internal model approach to cooperative robust output regulation for linear uncertain time‐delay multiagent systems

“…Remark Assumptions to are standard ones, and they are needed in Su et al even if there are no communication delay and input delay. Assumption is additional, and it is made so that the delayed system can be stabilized by using the low gain method introduced in Zhou et al…”

Stabilization of Discrete-Time Systems With Multiple Actuator Delays and Saturations

“…Notice that, in view of (25), we have (33) by which and inequality (116), the inequality in (32) can be continued as (34) where is related with (35) It follows that (36) By Jensen inequality in Lemma 2, we can compute (37) where . Denote .…”

“…In this paper, motivated by our recent work on stabilization of continuous-time time-delay systems [17], [37], [38], [39], [40], we consider global and semi-global stabilization problems for discrete-time linear systems with multiple delays and saturations. The truncated predictor feedback (TPF) approach proposed in [39], [40] for continuous-time time-delay systems will be generalized to discrete-time setting to study the concerned problems.…”

On higher-order truncated predictor feedback for linear systems with input delay

“…The idea is as follows. Let F = F ( γ ) be of order 1 with respect to γ , namely, Particularly, F can be chosen as F = − B T P with P = P ( γ ) being the unique positive definite solution to the parametric algebraic Riccati equation As a result, the first term u 1 ( t ) = F e Aτ x ( t ) in u ( t ) and the control u ( t ) itself are ‘of order 1’ with respect to γ , namely, …”