CONSTRUCTING ROBUST SLIDING SURFACES FOR QUADRATICALLY STABILIZABLE UNCERTAIN LINEAR SYSTEMS: A REDUCED ORDER DYNAMICS ASSIGNMENT APPROACH BASED ON SVD OF THE PROJECTIONS ON CONTROL INPUT RANGE SPACE

摘要

This work is concerned with the problem of designing stable invariant subspaces for the construction of discontinuity surfaces in variable structure control (VSC) of uncertain systems. In this paper, A new reduced order dynamics assignment method to design the closed loop systems, such as the model following control systems and VSC systems with sliding mode, having desirable behavior in tracking or regulation even if in presence of mismatched parameter uncertainty is developed based on quadratic stability and using singular value decompositions of the projections on control input range space and the corresponding complementary projections in state space. The robust sliding hyper-plane is constructed from a Riccati inequality associated with quadratic stabilizability of subsystem induced in quotient space of state space by control input range space. The study has been motivated by the observation that a basic operator associated with the assignment of dynamics in feedback control system qualifies as a projector. Projector theory provides a neat method for analysis and design of VSCS to construct the sliding manifolds in class of differentiable manifolds. Reducibility and invariance properties of projections make them very attractive to decompose a dynamic system into lower order two subsystems decoupled from each other, so we get deep insight into problems in analysis and design tasks of control systems and more information about dynamics incorporated with "modes' and eigenvectors represent intrinsic properties of dynamical systems.