State-energy-constrained controller design for uncertain semi-state systems and its application in mechanical system control

Abstract

The state-energy-constrained controller design for uncertain semi-state systems and its application in mechanical system control is studied in this paper. The objective is to get a sampled-data-based controller, with which the system is state-energy-constrained in a finite-time interval and has a given anti-disturbance performance. First, by adopting the matrix convex sets and data sampling, a sampled-data-based model for uncertain semi-state systems is obtained. Second, by considering those state-energy-constraints in real systems, the finite-time stability theory is utilized in the system analysis, and some sufficient conditions are achieved for uncertain semi-state systems with sampled data to be stabilizable. If these conditions are solvable, the sampled-data-based state-feedback controller can be gotten, such that the controlled system has an H-infinite performance, and the state energy is constrained in a finite-time interval. Finally, the obtained theorem is used to control some mechanical systems, and the results show that the controller obtained by the theorem in this paper can effectively attenuate the vibration of those mechanical systems and constrains their state-energies in a finite-time interval.