Effects of small delays on stability of singularly perturbed systems
نویسنده
چکیده
A small delay in the feedback loop of a singularly perturbed system may destabilize it; however, without the delay, it is stable for all small enough values of a singular perturbation parameter . Su3cient and necessary conditions for preserving stability, for all small enough values of delay and , are obtained in two cases: in the case of delay proportional to and in the case of independent delay and . In the second case, the su3cient conditions are given in terms of an LMI. A delay-dependent LMI criterion for the stability of singularly perturbed di erential–di erence systems is derived. ? 2002 Elsevier Science Ltd. All rights reserved.
منابع مشابه
Stability of singularly perturbed functional-differential systems: spectrum analysis and LMI approaches
A singularly perturbed linear functional-differential system is considered. The delay is assumed to be small of the order of a small parameter multiplying a part of derivatives in the system. It is ‘not assumed that the fast subsystem is asymptotically stable’. Two approaches to the study of the exponential stability of the singularly perturbed system are suggested. The first one treats systems...
متن کاملInput-to-State Stability of Singularly Perturbed Control Systems with Delays
We study the input-to-state stability of singularly perturbed control systems with delays. By using the generalized Halanay inequality and Lyapunov functions, we derive the input-to-state stability of some classes of linear and nonlinear singularly perturbed control systems with delays.
متن کاملRobust Stability of Singularly Perturbed Systems with State Delays
In this paper, robust stability of uncertain singularly perturbed systems with state delays is studied. Based on Lyapunov-Krasovskii stability theorem and linear matrix inequality (LMI) technique, sufficient conditions are given to guarantee that systems are asymptotically stable, and explicit stability bounds are attained by solving convex optimization problem. Numerical example is presented t...
متن کاملAn efficient numerical method for singularly perturbed second order ordinary differential equation
In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It ...
متن کاملA Novel Approach to Exact Slow-Fast Decomposition of Linear Singularly Perturbed Systems with Small Delays | SIAM Journal on Control and Optimization | Vol. 55, No. 1 | Society for Industrial and Applied Mathematics
A linear time-invariant singularly perturbed system with multiple pointwise and distributed small time delays is considered. A novel (direct) approach to exact slow-fast decomposition of this system is proposed. In contrast with the existing method, this approach uses neither a preliminary transformation of the original differential system to an integral one nor rather complicated integral mani...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Automatica
دوره 38 شماره
صفحات -
تاریخ انتشار 2002