Measurable Disturbance Rejection with Stability in Continuous-Time Switched Linear Systems under Dwell-Time Switching

This work deals with rejection of disturbance inputs accessible for measurement in continuous-time switched linear systems with dwell-time constraints on the switching signals. The measurable disturbance rejection problem is stated as the problem of finding a dynamic feedforward switched compensator achieving zero output and exponential stability of the compensated switched linear system over a class of switching signals with a sufficiently large dwell-time, in the presence of any admissible measurable disturbance input. The synthesis of the compensator is based on a pair of sufficient conditions which respectively address the structural issue and the stabilizability issue. The former condition is expressed in geometric terms as the inclusion of the image of the disturbance input matrix in the sum of the so-called maximal robust controlled invariant subspace and the image of the control input matrix, for all the modes of the given switched system. The second condition is expressed as the exponential stabilizability under dwell-time switching of the internal switched dynamics of the maximal robust controlled invariant subspace.