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Abstract: In this study, we shall be concerned with a non-autonomous second-order Hamiltonian system. Some criteria for guaranteeing the existence and uniqueness of T-periodic classical solution of this system are presented by employing the least action principle, the Saddle Point Theorem and some analysis techniques. [Copyright &y& Elsevier]

This paper mainly presents Routh-type table test methods for zero distribution of polynomials with commensurate fractional degrees on the left-half plane, right-half plane and imaginary axis in the complex plane. The proposed tabular methods are derived for extension and generalization of the Routh test, which is widely used in controls for zero distribution of polynomials with integer degrees. Singular cases are discussed and handled efficiently and simply. Necessary and sufficient conditions for the second singular case are completely analyzed in terms of symmetric zeros. A particular property is revealed that a polynomial with commensurate fractional degrees without pure imaginary zero may still be stable in the presence of the second singular case, which is impossible for a real polynomial with integer degrees. Furthermore, we present a test to solve the zero distribution problem with respect to general sector region for polynomials with commensurate fractional degrees and real/complex coefficients. Finally, numerical examples are given to illustrate the correctness and effectiveness of the results. The proposed methods have broad application areas, including various systems, circuits and control. [ABSTRACT FROM AUTHOR]

This paper studies stability analysis of a class of integral delay systems (IDSs) with multiple exponential kernels. Some coupled linear matrix inequalities based sufficient stability conditions are firstly obtained with the help of the Lyapunov–Krasovskii functional approach. The obtained results include several existing ones as special cases if the corresponding IDSs are simplified. Characteristic equations based necessary and sufficient conditions are then established for a special class of IDSs. Three numerical examples show the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

Fractional calculus is an efficient tool, which has the potential to improve the performance of gradient methods. However, when the first order gradient direction is generalized by fractional order gradient one, the corresponding algorithm converges to the fractional extreme point of the target function which is not equal to the real extreme point. This drawback critically hampers the application of this method. To solve such a convergence problem, the current paper analyzes the specific reasons and proposes three possible solutions. Considering the long memory characteristics of fractional derivative, short memory principle is a prior choice. Apart from the truncation of memory length, two new methods are developed to reach the convergence. The former is the truncation of the infinite series, and the latter is the modification of the constant fractional order. Finally, six illustrative examples are performed to illustrate the effectiveness and practicability of proposed methods. [ABSTRACT FROM AUTHOR]

This paper mainly investigates the issue of parameters identification for continuous time fractional order Hammerstein systems. When the commensurate order of linear part in system is prior information, two estimation algorithms are proposed to identify the parameters. Both methods use filters to obtain the derivative of the continuous time signal: one based on the Poisson filter and the other using the auxiliary model to construct the filter. Afterwards, the commensurate order update law is given, which contains the relationship between parameters and orders. In addition, due to the existence of fractional order terms, an irrational item will be introduced, and this paper gives a detailed mathematical derivation to discuss this issue. The effectiveness of proposed methods is demonstrated by the numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the stabilization problem of singular fractional order systems with order α ∈ (0, 2). In addition to the sufficient and necessary condition for observer based control, a sufficient and necessary condition for output feedback control is proposed by adopting matrix variable decoupling technique. The developed results are more general and efficient than the existing works, especially for the output feedback case. Finally, two illustrative examples are given to verify the effectiveness and potential of the proposed approaches. [ABSTRACT FROM AUTHOR]

Abstract For multichannel signal filtering or detection in unknown noise, it is usually difficult to obtain sufficient independent and identically distributed (IID) training data in real-world applications, which considerably degrades the performance of adaptive algorithms. In this paper, we consider the problem of subspace signal filtering and detection in sample-starved environment. A simple reduced-dimension approach is adopted, which alleviates the requirement of IID training data. First, the test and training data are projected onto the signal subspace. Then we adopt the criterion of the generalized likelihood ratio test (GLRT) to devise a detector, which can also serve as a filter. The resulting detector can properly work in sample-starved environment, where the number of IID training data is less than the dimension of the test data. Moreover, the devised approach is superior to the existing adaptive subspace processor in filtering and detection, even in some sample-abundant situations. Analytical expressions for the probabilities of detection and false alarm are derived for the proposed approach. Numerical examples are given to verify its effectiveness. [ABSTRACT FROM AUTHOR]

Abstract: The research of robust stability for fractional order linear time-invariant (FO-LTI) interval systems with uncertain parameters has become a hot issue. In this paper, it is the first time to consider robust stability of uncertain parameters FO-LTI interval systems, which have deterministic linear coupling relationship between fractional order and other model parameters. Linear matrix inequalities (LMI) methods are used, and a criterion for checking asymptotical stability of this class of systems is presented. One numerical illustrative example is given to verify the correctness of the conclusions. [Copyright &y& Elsevier]