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Register a new userSufficient and necessary conditions for stabilizing singular fractional order systems with partially measurable state
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This paper is concerned with the stabilization problem of singular fractional order systems with order $alphain(0,2)$. 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.
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This paper has been withdrawn. This paper focuses on the admissibility condition for fractional-order singular system with order $alpha in (0,1)$. The definitions of regularity, impulse-free and admissibility are given first, then a sufficient and necessary condition of admissibility for fractional-order singular system is established. A numerical example is included to illustrate the proposed condition.
The present work establishes necessary and sufficient conditions for a nonlinear system with two inputs to be described by a specific triangular form. Except for some regularity conditions, such triangular form is flat. This may lead to the discovery of new flat systems. The proof relies on well-known results for driftless systems with two controls (the chained form) and on geometric tools from exterior differential systems. The paper also illustrates the application of its results on an academic example and on a reduced order model of an induction motor.
We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating such a transformation as differential equations that give new variables in terms of original ones. The obtained results generalise the well-known and widely used inverse function theorem. Taking into account that field transformations are ubiquitous in modern physics and mathematics, our criteria for invertibility will find many useful applications.
This paper deals with the stability analysis problem of discrete-time switched linear systems with ranged dwell time. A novel concept called L-switching-cycle is proposed, which contains sequences of multiple activation cycles satisfying the prescribed ranged dwell time constraint. Based on L-switching-cycle, two sufficient conditions are proposed to ensure the global uniform asymptotic stability of discrete-time switched linear systems. It is noted that two conditions are equivalent in stability analysis with the same $L$-switching-cycle. These two sufficient conditions can be viewed as generalizations of the clock-dependent Lyapunov and multiple Lyapunov function methods, respectively. Furthermore, it has been proven that the proposed L-switching-cycle can eventually achieve the nonconservativeness in stability analysis as long as a sufficiently long L-switching-cycle is adopted. A numerical example is provided to illustrate our theoretical results.
Matrix regularity is a key to various problems in applied mathematics. The sufficient conditions, used for checking regularity of interval parametric matrices, usually fail in case of large parameter intervals. We present necessary and sufficient conditions for regularity of interval parametric matrices in terms of boundary parametric hypersurfaces, parametric solution sets, determinants, real spectral radiuses. The initial n-dimensional problem involving K interval parameters is replaced by numerous problems involving 1<= t <= min(n-1, K) interval parameters, in particular t=1 is most attractive. The advantages of the proposed methodology are discussed along with its application for finding the interval hull solution to interval parametric linear system and for determining the regularity radius of an interval parametric matrix.
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