Abstract
We investigate the problem of robust exponential stability analysis for uncertain impulsive switched linear systems with time-varying delays and nonlinear perturbations. The time delays are continuous functions belonging to the given interval delays, which mean that the lower and upper bounds for the time-varying delays are available, but the delay functions are not necessary to be differentiable. The uncertainties under consideration are nonlinear time-varying parameter uncertainties and norm-bounded uncertainties, respectively. Based on the combination of mixed model transformation, Halanay inequality, utilization of zero equations, decomposition technique of coefficient matrices, and a common Lyapunov functional, new delay-range-dependent robust exponential stability criteria are established for the systems in terms of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness of the proposed method.
Highlights
The problem of stability analysis for dynamical systems with time delays and uncertainties has been intensively studied since these systems often occur in many industrial systems such as chemical processes, biological systems, population dynamics, neural networks, large-scale systems, and network control systems
We investigate the problem of robust exponential stability analysis for uncertain impulsive switched linear systems with timevarying delays and nonlinear perturbations
Much attention has been paid to stability analysis of the uncertain linear systems with interval timevarying delay [3,4,5,6]
Summary
The problem of stability analysis for dynamical systems with time delays and uncertainties has been intensively studied since these systems often occur in many industrial systems such as chemical processes, biological systems, population dynamics, neural networks, large-scale systems, and network control systems. There has been growing interest in stability analysis and controller design for time-delay systems. Much attention has been paid to stability analysis of the uncertain linear systems with interval timevarying delay [3,4,5,6]. In [5], the authors studied the delaydependent stability problem for uncertain linear systems with interval time-varying delay. Robust stability analysis of uncertain linear systems with time-varying delays and nonlinear perturbations has received the attention of a lot of theoreticians and engineers in this field over the last few decades [7,8,9,10,11,12,13,14].
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