State feedback switched control of discrete-time switched linear systems with application to networked control

This paper treats the state feedback switched control design problem for discrete-time switched linear systems. More specifically, the control goal is to design a set of state feedback gains together with a state dependent switching function assuring stability and H₂, H_∞ performance indexes. The conditions are based on Lyapunov or Riccati-Metzler inequalities which although are difficult to solve for a large number of subsystems, allow the derivation of simpler alternative conditions expressed by LMIs whenever a scalar variable is fixed. This theory is well adapted to treat an important networked control problem known as discrete-time self-triggered control design problem, where the switching rule is responsible for the scheduling of the sampling periods to be considered in the communication channel at each sampling time instant in order to improve performance. This method is compared theoretically with others from literature. Academical examples are used for comparisons and to show the validity of the proposed technique in both contexts, switched and networked control systems.