UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

Thermally Induced Instability of Laminated Beams and Plates

A theoretical investigation of dynamic stability for linear elastic structures due to non-uniform, time and space-dependent stochastic temperature fields is presented. The study is based on the reformulation of stochastic stability problems as a stability of Itoˆ type equations in some appropriate Hilbert space and is adopted for stability problems of structures with time and space-dependent stochastic coefficients. Uniform stochastic stability criteria of the structure equilibrium are derived using the Liapunov direct method. The energy-like functional and the generalized ltoˆ lemma are used to derive the sufficient stability conditions of the equilibrium state. A symmetrically laminated crossply plate subjected to the wide-band Gaussian temperature distribution and a laminated beam subjected to local short-time heatings are analysed in detail.

STABILITY OF EULER, LAGRANGE AND KOVALEVSKAYA GYROS IN A NEWTONIAN CENTRAL FORCE FIELD WITH SECOND ORDER TERMS

The stability of the permanent rotation of the Euler, Lagrange and Kovalevskaya gyros about a fixed point in the Newtonian central force field is investigated by Liapunov direct method, which improve Leimanis’ and Rumiantsev’s result of stability conditions. For the sake of high accuracy, the first and second order terms of R-1 expressed by potential energy of the Newtonian central force field have been considered, where the R is the distance from the fixed point to the center of attraction.

STABILITY OF RATE GYRO IN A VEHICLE WITH UNCERTAIN ANGULAR VELOCITY AND ACCELERATION

Using the Liapunov direct method, we study the stability of motion of a single-axis rate gyro mounted on a space vehicle which is simultaneously accelerating (ω)x(t)) with respect to the output axis and rotating (ωz(t)) about the spin axis of gyro. The analytical relations, which must be satisfied by the gyro parameters, are obtained for the asymptotical stability of the gimbal motion. In addition, by using a fourth-order Runge-Kutta numerical method, the trajectories of motions of a rate gyro are obtained to verify its stability.

Multivariable Adaptive Control for Turbojet Engines

Integrated flight and propulsion control systems will require propulsion systems to reduce in time to accelerate engine and to improve transient performance for a full flight envelope operation. A multivariate model reference adaptive control (MRAC) scheme is proposed in this paper. Acceleration time is reduced by uptrimming engine pressure ratio in some operating conditions and in parts of the flight envelope where excess stall margin and turbine temperature margin exist. The MRAC scheme is obtained by using Liapunov direct method. Simulation studies are performed for a two-spool turbojet engine. The satisfactory transient responses are obtained at different operating points from idle to maximum dry power in flight envelope which shows good robustness for unmodelled dynamics of nonlinear engine. Simulation results also show the good effectiveness of reducing interaction in multivariable system with significant coupling. Using the Multivariable MRAC controller, the engine acceleration time is reduced about 16 percent in comparison with the conventional engine controller.

Stability Analysis of the Motion of a Tuned Gyroscope

In this paper, we use the Liapunov direct method to study the stability of motion of the rotor of a single-gimbal, elastically supported tuned gyroscope with the input rate ø̇1 = ø̇2 = 0 in three cases: (1) rotor-gimbal damping coefficients D1 = D2 = 0, rotor winding coefficient Dw = 0; (2) D1 ≠ 0, D2 ≠ 0, Dw = 0; (3) D1 ≠ 0, D2 ≠0, Dw ≠ 0.