Further results on stability and stabilisation of linear systems with state and input delays

This article concerns the stability and stabilisation of a linear system with both state and input delays. First, the combination of an augmented Lyapunov functional and the free-weighting-matrix technique yields a new delay-independent stability criterion that includes the widely used one as a special case. This criterion is then extended to a new delay-dependent stability criterion by employing an integral inequality. Based on that, a stabilisation approach to design a state feedback controller is presented that requires no parameter tuning, as is needed with some existing methods. Finally, numerical examples illustrate that the method is effective and is an improvement over existing ones

Delay-dependent H∞ control of linear discrete-time systems with an interval-like time-varying delay

The free-weighting-matrix approach is developed to study the H control of linear discrete-time systems with an interval-like time-varying delay. First, a delay- and range-dependent criterion for a given H performance is derived. Second, a memoryless H state-feedback controller is designed based on a performance analysis. Finally, two numerical examples demonstrate the effectiveness of the proposed method and show that both the upper bound and range of an interval-like time-varying delay affect the stability and/or H performance of a system

Delay-dependent stabilization of linear systems with time-varying state and input delays

The integral-inequality method is a new way of tackling the delay-dependent stabilization problem for a linear system with time-varying state and input delays: ẋ(t)=Ax(t)+A1x(t-h1(t))+B1u(t)+B2u(t-h2(t)). In this paper, a new integral inequality for quadratic terms is first established. Then, it is used to obtain a new state- and input-delay-dependent criterion that ensures the stability of the closed-loop system with a memoryless state feedback controller. Finally, some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective, even though neither (A,B1) nor (A+A1,B1) is stabilizable