Partial stabilisation of semilinear systems using bounded controls

Abstract

This paper studies a partial stabilisation problem for distributed semilinear systems. This consists of steering only a part of the system’s state to its equilibrium. Constrained controls are proposed to force the desired part of the state to approach the equilibrium. Necessary and sufficient conditions for weak and strong partial stabilisation are given. Applications are presented.

Keywords:

• partial stabilisation
• nonlinear control
• constrained control
• semilinear systems