L 2-Gain analysis and control synthesis of uncertain discrete-time switched linear systems with time delay and actuator saturation

The problem of L 2-gain analysis and control synthesis is studied for a class of uncertain discrete-time switched linear systems with time delay and saturating actuators by using the multiple Lyapunov functions method. With the state feedback controllers adopted beforehand, an analysis condition on disturbance tolerance is derived under which the operating state trajectory with zero initial condition will remain inside a bounded set in its proximity. Then with this condition at hand, the largest disturbance tolerance level is determined via the solution of a constrained optimisation problem. Then, a sufficient condition for the restricted L 2-gain over the set of tolerable disturbances is derived. The smallest upper bound on the restricted L 2-gain is also obtained by solving a constrained optimisation problem. Furthermore, when controller gain matrices are design variables, these optimisation problems are adjusted for solving the control design task. An illustrative numerical example is given to demonstrate the feasibility and effectiveness of the proposed method.