A 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
نویسنده
چکیده
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 manifold and operator techniques. Moreover, the approach of the present paper does not assume the exponential stability of the fast subsystem. Based on this decomposition, an exact slow-fast decomposition of the spectrum of a singularly perturbed system with a single pointwise small delay is carried out. Using the theoretical results, the stability of a multilink single-sink optical network is analyzed.
منابع مشابه
Near-Optimal Controls of a Fuel Cell Coupled with Reformer using Singular Perturbation methods
A singularly perturbed model is proposed for a system comprised of a PEM Fuel Cell(PEM-FC) with Natural Gas Hydrogen Reformer (NG-HR). This eighteenth order system is decomposedinto slow and fast lower order subsystems using singular perturbation techniques that provides tools forseparation and order reduction. Then, three different types of controllers, namely an optimal full-order,a near-opti...
متن کاملADAPTIVE FUZZY TRACKING CONTROL FOR A CLASS OF NONLINEAR SYSTEMS WITH UNKNOWN DISTRIBUTED TIME-VARYING DELAYS AND UNKNOWN CONTROL DIRECTIONS
In this paper, an adaptive fuzzy control scheme is proposed for a class of perturbed strict-feedback nonlinear systems with unknown discrete and distributed time-varying delays, and the proposed design method does not require a priori knowledge of the signs of the control gains.Based on the backstepping technique, the adaptive fuzzy controller is constructed. The main contributions of the paper...
متن کاملA method based on the meshless approach for singularly perturbed differential-difference equations with Boundary layers
In this paper, an effective procedure based on coordinate stretching and radial basis functions (RBFs) collocation method is applied to solve singularly perturbed differential-difference equations with layer behavior. It is well known that if the boundary layer is very small, for good resolution of the numerical solution at least one of the collocation points must lie in the boundary layer. In ...
متن کاملExact slow± fast decomposition of a class of non-linear singularly perturbed optimal control problems via invariant manifolds
We study a Hamilton± Jacobi partial di erential equation, arising in an optimal control problem for an a ne non-linear singularly perturbed system. This equation is solvable i there exists a special invariant manifold of the corresponding Hamiltonian system. We obtain exact slow± fast decomposition of the Hamiltonian system and of the special invariant manifold into slow and fast components....
متن کاملCheap Control Problem of Linear Systems With Delays: A Singular Perturbation Approach
A quadratic cheap control of linear systems with multiple state delays is considered. This optimal control problem is transformed to an optimal control problem of singularly perturbed systems. A composite suboptimal control of the latter is designed based on its asymptotic decomposition into two much simpler parameter-free subproblems, the slow and fast ones. Using this composite control, a sub...
متن کامل