A Rigorous Solution for Finite-State Inflow throughout the Flowfield

In this research, the Hseih/Duffy model is extended to all three velocity components of inflow across the rotor disk in a mathematically rigorous way so that it can be used to calculate the inflow below the rotor disk plane. This establishes a complete dynamic inflow model for the entire flow field with finite state method. The derivation is for the case of general skewed angle. The cost of the new method is that one needs to compute the co-states of the inflow equations in the upper hemisphere along with the normal states. Numerical comparisons with exact solutions for the z-component of flow in axial and skewed angle flow demonstrate excellent correlation with closed-form solutions. The simulations also illustrate that the model is valid at both the frequency domain and the time domain. Meanwhile, in order to accelerate the convergence, an optimization of even terms is used to minimize the error in the axial component of the induced velocity in the on and on/off disk region. A novel method for calculating associate Legendre function of the second kind is also developed to solve the problem of divergence with the iterative method. An application of the new model is also conducted to compute inflow in the wake of a rotor with a finite number of blades. The velocities are plotted at different distances from the rotor disk and are compared with the Glauert prediction for axial flow and wake swirl. In the finite-state model, the angular momentum does not jump instantaneously across the disk, but it does transition rapidly across the disk to correct Glauert value

New results on stabilization of Markovian jump systems with time delay

This paper studies the problem of stochastic stabilization for a class of Markovian jump systems with time delay. A new delay-dependent stochastic stability criterion on the stochastic stability of the system is derived based on a novel Lyapunov–Krasovskii functional (LKF) approach. The equivalence and superiority to existing results are demonstrated. Then a state feedback controller, which guarantees the stochastic stability of the closed-loop system, is designed. Illustrative examples are provided to show the reduced conservatism and effectiveness of the proposed techniques

A generalized parameter-dependent approach to robust H∞ filtering of stochastic systems

This paper is concerned with the problem of robust H ∞ filtering for discrete-time stochastic systems with state-dependent stochastic noises and deterministic polytopic parameter uncertainties. We utilize the polynomial parameter-dependent approach to solve the robust H ∞ filtering problem, and the proposed approach includes results in the quadratic framework that entail fixed matrices for the entire uncertain domain and results in the linearly parameter-dependent framework that use linear convex combinations of matrices as special cases. New linear matrix inequality (LMI) conditions obtained for the existence of admissible filters are developed based on homogeneous polynomial parameter-dependent matrices of arbitrary degree. As the degree grows, a test of increasing precision is obtained, providing less conservative filter designs. A numerical example is provided to illustrate the effectiveness and advantages of the filter design methods proposed in this paper. © Birkhäuser Boston 2008

New results on stability analysis and stabilization of time-delay continuous Markovian jump systems with partially known rates matrix

Summary In this note, the problems of stability analysis and controller synthesis of Markovian jump systems with time-varying delay and partially known transition rates are investigated via an input-output approach. First, the system under consideration is transformed into an interconnected system, and new results on stochastic scaled small-gain condition for stochastic interconnected systems are established, which are crucial for the problems considered in this paper. Based on the system transformation and the stochastic scaled small-gain theorem, stochastic stability of the original system is examined via the stochastic version of the bounded realness of the transformed forward system. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a precise approximation of the time-varying delay and the new result on the stochastic scaled small-gain theorem. The proposed stability condition is demonstrated to be much less conservative than most existing results. Moreover, the problem of stabilization is further solved with an admissible controller designed via convex optimizations, whose effectiveness is also illustrated via numerical examples

New synchronization stability of complex networks with an interval time-varying coupling delay

In this brief, the problem of synchronization stability analysis for complex dynamical networks with a time-varying coupling delay is studied. The delay considered in this brief is assumed to vary over an interval where the lower and upper bounds are known. By dividing the interval time-varying delay into a constant and a time-varying part and using a delay-partitioning approach, a new Lyapunov-Krasovskii functional is constructed. Based on this, a new delay-range-dependent criterion is obtained in terms of linear matrix inequalities. A numerical example is provided to show the effectiveness of the proposed results