Disturbance decoupling in nonlinear hybrid systems

The paper studies the problem of disturbance decoupling of nonlinear hybrid systems. The hybrid systems under consideration are switched systems that consist of finite automaton, which defines the switching rule, a set of nonlinear discrete-time systems and the so-called mode activator, that defines an input for the automaton. Such systems allow to handle more complex switching rules than just time- or state-dependent switchings. The goal of the paper is to achieve the disturbance decoupling by dynamic measurement feedback. The advantage of such feedback is that it does not require estimations of state variables. Sufficient conditions are found under which there exists a dynamic measurement feedback, such that in the closed-loop system the controlled output of the hybrid system does not depend on the disturbance. An algebraic approach called functions' algebra is used, which can address in a similar manner both discrete-time systems and discrete-event systems (finite automaton).