Improvement on robust control of uncertain systems with time-varying input delays

Abstract

The problem of robust control is considered for uncertain systems with time-varying input delays. A new Lyapunov -Krasovskii functional is used together with a neutral transformation to design a robust controller for larger bounds on plant uncertainties than permitted by a recently published method. Numerical examples verify the analysis results. IntroductionRecently, the stability of uncertain systems with control input delay was investigated in Cheres et al. . The drawback is that the exact value of the time delay must be known. For time-varying delays, Lyapunov-Krasovskii functionals have been applied [9 -14]. However, the choice of Lyapunov -Krasovskii functional yields different bounds on the time delay for stability [15]. For systems with timevarying input delays, a delayed feedback control design method was proposed using the Lyapunov -Krasovskii functional approach and a neutral transformation, which gave a conservative bound on the allowable time delay [7]. One method to reduce conservativeness is to construct the Lyapunov -Krasovskii functional with a better distribution of the time delays [16].In this paper, the problem of robust control for linear systems with input delays is studied. A general method is proposed that combines a novel Lyapunov -Kranovoskii functional and a neutral transformation to obtain sufficient conditions for closed-loop robustness. These conditions are then transformed into an LMI problem to solve for the robust controller.The advantages of the new Lyapunov -Kranovoskii functional are explained and demonstrated on examples. The method allows time delays that can change at any rate and allows larger bounds on plant uncertainties than are achieved by the method of Yue and Han [7].Notation: Throughout this paper, the superscripts '21' and 'T' stand for the inverse and transpose of a matrix, respectively, R n denotes an n-dimensional Euclidean space, R mÂn is the set of all m  n real matrices, P . 0 means that the matrix P is positive definite, I is an appropriately dimensioned identity matrix, and the symmetric terms in a symmetric matrix are denoted by Ã, for example Problem statementConsider the following uncertain system with a timevarying delay

Adaptive control for a class of nonlinear systems with time-varying delays in state and input

“…In [13], γ max = 8.4602 and in [14] the maximum allowable value is γ max = 9.1574 for the robust controller.…”

“…Fig. 1 shows the response of the closed-loop system with the uncertain bound γ = 14 that exceeds the maximum required in [12,14]. Case 2 τ (t) is time-varying and 0…”

Sliding Mode Control for Linear Systems with Time-Varying Input and State Delays

“…(15) in Theorem 1 has solutions P, Q, R 1 , R 2 and Y and the sliding surface is given by (4). Then the trajectory of the closed-loop system (1) can be driven onto the sliding surface in finite time with the control…”

“…The study of input delay systems also has obtained some attention, for example, the robust stabilization problem of continuous systems with unknown input delay or time-varying input delay were concerned in [20,22] and [21], respectively. Then, the input delay stabilization results were improved in [15]. Furthermore, the feedback a of a general class of well posed linear systems with both state and input delays in Banach spaces was studied in [9].…”

“…Then, using the Matlab LMI Control Toolbox to solve the LMIs(15) in Theorem 1, the solution is obtained as follows:The largest state delay is τ M = 0.2 and the largest input delay is d M = 0.1. Moreover, a stabilizing equivalent control law is given by…”