Stabilization and control analysis of distributed parameter systems

Stability is one of the main concerns in control theory for distributed parameter systems. The characteristics of these systems are studied by using semigroup properties of a set of partial differential equations. The Lyapunov stability method pertinent to distributed parameter dynamical systems is presented. This stability technique is applied to two examples of such systems with parabolic and hyperbolic dynamic equations. Based on these analyses, the stability of a simplified model of a magneto-plasma-dynamic (MPD) thruster is determined. Controllability and observability of abstract dynamical systems, as applied to the two considered classes of distributed parameter systems, are discussed. Stabilization with distributed control, using a body force , for symmetric hyperbolic systems is analyzed. Moreover, stabilization by means of a finite number of colocated sensors and actuators at the boundary, for symmetric hyperbolic systems and systems of contraction semigroups, is derived. A formulation for finite order feedback control at strategic points of a distributed parameter system is derived. This new feedback control is applied to the Euler-Bernoulli beam, as a classical distributed parameter system. Simulation results indicate that this control technique is capable of stabilizing all modes of the beam while avoiding the control spillover problem, which is associated with other techniques proposed for control of distributed parameter systems