A switching supervisory control design for uncertain discrete time-delay systems

This paper presents an adaptive switching supervisory control scheme for highly uncertain discrete-time systems with time-varying state delay and time-varying parameters. The uncertainties appear in the system matrices and the system is assumed to be subject to the external bounded disturbances. It is supposed that a set of stabilizing controllers are available (which are designed off-line) to stabilize the system in the whole uncertain parameter space. To find a supervisory control scheme, it is initially assumed that the system parameters and delay are fixed. A switching algorithm is then proposed to stabilize the system. Next, by modifying the proposed algorithm, the stability analysis of the system with time-varying parameters and time-varying delay is carried out. Furthermore, an upper bound on the permissible rate of change of the system parameters and delay to maintain stability of the closed-loop system is obtained. Simulation results are presented to show the efficacy of the proposed switching scheme.