Results 151 to 160 of about 1,207 (185)

Singularly perturbed normal operators

Ukrainian Mathematical Journal, 1999
We present a generalization of the definition of singularly perturbed operators to the case of normal operators. To do this, we use the idea of normal extensions of a prenormal operator and prove the relation for resolvents of normal extensions similar to the M. Krein relation for resolvents of self-adjoint extensions.
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Controlled Singularly Perturbed Systems

1990
Many control problems can be modelled by systems of differential equations where the state variable can be divided into two coupled groups. Those in the first group change at a “normal” rate, and those in the second group change at a much “faster” rate.
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Singularly Perturbed Systems of Volterra Equations

Journal of Applied Analysis, 2002
This paper studies the behaviour of the solution \(u(t,\varepsilon)\) of the system of Volterra integral equations \[ \varepsilon u(t) = f(t) + \int_0^t A(t,s)u(s)\,ds, \quad 0 \leq t \leq T, \] as the positive parameter \(\epsilon\) tends to zero. Both \(f\) and \(A\) are continuous, and the eigenvalues of \(A(t,t)\) are supposed to be negative.
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Singularly Perturbed Volterra Integro-differential Equations

Quaestiones Mathematicae, 2002
Several investigations have been made on singularly perturbed integral equations. This paper aims at presenting an algorithm for the construction of asymptotic solutions and then provide a proof asymptotic correctness to singularly perturbed systems of Volterra integro-differential equations.
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Suboptimization of Singularly Perturbed Control Systems

SIAM Journal on Control and Optimization, 1992
The singularly perturbed control system \(\dot z=f_ 1(z,y,u)\), \(z(0)=z_ 0\), \(\varepsilon\dot y=f_ 2(z,y,u)\), \(y(0)=y_ 0\), is studied and compared with the `reduced system' \(\dot z=f_ 1(z,\psi(z,u),u)\), \(z(0)=z_ 0\), where \(y=\psi(z,u)\) is the root of the static equation \(0=f_ 2(z,y,u)\). It is shown that the reduced system approximates the
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Interior Estimates for Singularly Perturbed Problems

Zeitschrift für Analysis und ihre Anwendungen, 1984
The solution of the Dirichlet problem for a singularly perturbed elliptic differential equation \epsilon L_1u + L_0u = h of order 2m converges, for
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Singularly Perturbed Discontinuous Systems

1992
One of the major obstacles in the use of efficient tools for designing control systems is the high order of equations that describe their behaviour. In many cases they may be reduced to a lower order model by neglecting small time constants or rejecting fast components of the system overall motion.
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Finite-Time Fuzzy Control for Nonlinear Singularly Perturbed Systems With Input Constraints

IEEE Transactions on Fuzzy Systems, 2022
Feng Li, Wei-Xing Zheng, Shengyuan Xu
exaly  

Observer-Based Sliding Mode Control for Networked Fuzzy Singularly Perturbed Systems Under Weighted Try-Once-Discard Protocol

IEEE Transactions on Fuzzy Systems, 2022
Jing Wang, Chengyu Yang, Jianwei Xia
exaly  

Finite-Time Event-Triggered Stabilization for Discrete-Time Fuzzy Markov Jump Singularly Perturbed Systems

IEEE Transactions on Cybernetics, 2023
Wenhai Qi, Guangdeng Zong, Shun-Feng Su
exaly