Discrete-Time Switched Linear Systems State Feedback Design With Application to Networked Control

This technical note addresses the state feedback switched control design problem for discrete-time switched linear systems. More specifically, the control goal is to jointly design a set of state feedback gains and a state dependent switching function, ensuring H₂ and H_∞ guaranteed performance. The conditions are based on Lyapunov or Riccati-Metzler inequalities, which allow the derivation of simpler alternative conditions that are expressed as LMIs whenever a scalar variable is fixed. The theoretical results are well adapted to deal with the self-triggered control design problem, where the switching rule is responsible for the scheduling of multiple sampling periods, to be considered in the communication channel in order to improve performance. This method is compared to others from the literature. Examples show the validity of the proposed technique in both contexts, switched and networked control systems.