Zeng Jianping

On common solutions of Riccati inequalities: for plannar case

Some examples are presented to show the significance of the study of the common positive definite solutions to a set of algebraic Riccati inequalities (ARIs). A necessary and sufficient condition for the existence of common positive definite solutions of a set of second-order Riccati inequalities is derived. This condition provides a new algorithm of computing the common solutions of ARIs. Unlike LMI method, the computing collapse will not occur with the increase of the number of Riccati inequalities due to the fact that our approach handles the ARIs one by one rather than simultaneously.

Improvement of Robust Positive Realness for a Class of Uncertain Systems

This paper focuses on robust positive realness analysis and synthesis problem for a class of parameter uncertainty, which has a polynomial form and is a natural extension of the norm-bounded uncertainty. A sufficient condition of robust extended strictly positive realness(ESPR) is obtained for the class of linear uncertainty systems. Moreover, the solvability condition to robust ESPR control is provided via output feedback based on LMI. Furthermore, an approach can be given to design the output feedback controller via convex optimal algorithm.

Nonlinear stabilization control of tilt rotor UAV during transition flight based on HOSVD

Aiming at the transition progress of tilt rotor UAV and considering the characteristic that tilt angle leads the mode transition, a new control approach is proposed. Jacobian linearization is used at an appropriate quantity of equilibrium points chosen at equal interval in the range of tilt angle, then putting the resulting LTI systems into a tensor and discarding smaller and zero singular values together with their corresponding singular vectors through higher older singular value decomposition (HOSVD), reconstructing the reduced-rank tensor to obtain a polynomial system constructed by a finite number of vertexes and their weight functions. Based on SOS programming technique and Lyapunov stability theory, both the stability analysis and controller design problems are converted into solving a parameter-dependent linear matrix inequalities (LMI), which can be solved directly through SOS technique. Finally, the transition progress of the fixed wing mode to helicopter mode is simulated in the longitudinal channel, the result shows that the aircraft can complete the conversion mode flight accurately along the predetermined trajectory and the controller is robust to the variations of the aerodynamic parameters and external disturbance.