On the robust controlled invariant (Q1095850)

In order to characterize systems subject to parameter changes the robust controlled invariant is defined. It is an extended version of the controlled invariant which was already defined for time-invariant systems elsewhere by the authors [see J. Optimization Theory Appl. 3, 306-315 (1969; Zbl 0172.125)]. An algorithm to determine a maximum robust (A(p),\({\mathcal B}(p))\)- controlled invariant is presented. It is an extended version of the algorithm for the maximum (a,b)-controlled invariant contained in the paper cited above. The concept of robust self-bounded controlled invariant is introduced. It is an extension of the self-bounded controlled invariant which is effective to determine stability in the regulator synthesis without any use of eigenvectors or eigenspaces. As a typical application of the robust controlled invariant, the robust disturbance decoupling problem is presented. Since the plant is assumed to vary very slowly, it can be identified, and hence the state vector can be estimated through an observer. The control u can by synthesized as a function of the state vector x and the vector p which characterizes the parameter variation of the plant.