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478
The Sturm-Liouville eigenvalue problem is symmetric if the coefficients are even functions and the boundary conditions are symmetric. The eigenfunction is expressed in terms of orthonormal bases, which are constructed in a linear space of trial functions by using the Gram-Schmidt orthonormalization technique. Then an -dimensional matrix eigenvalue problem is derived with a special matrix , that is, if is odd.Based on the product formula, an integration method with a fictitious time, namely...
The purpose of this paper is to show that the method of controlled lagrangians and its hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...
The purpose of this paper is to show that the method of controlled
Lagrangians and its Hamiltonian counterpart (based on the notion
of passivity) are equivalent under rather general hypotheses. We
study the particular case of simple mechanical control systems
(where the underlying Lagrangian is kinetic minus potential
energy) subject to controls and external forces in some detail.
The equivalence makes use of almost Poisson structures (Poisson
brackets that may fail to satisfy the Jacobi identity)...
The existence of bounded solutions for equations x' = A(t)x + r(x,t) is proved, where the linear part is exponentially dichotomic and the nonlinear term r satisfies some weak conditions.
In this paper, the feedback control for a class of bilinear control systems with a small parameter is proposed to guarantee the existence of limit cycle. We use the perturbation method of seeking in approximate solution as a finite Taylor expansion of the exact solution. This perturbation method is to exploit the “smallness” of the perturbation parameter to construct an approximate periodic solution. Furthermore, some simulation results are given to illustrate the existence of a limit cycle for...
This paper is concerned with periodic solutions of first-order nonlinear functional differential equations with deviating arguments. Some new sufficient conditions for the existence of periodic solutions are obtained. The paper extends and improves some well-known results.
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