Input-to-state stability for discrete-time nonlinear switched singular systems

• Discrete-time nonlinear switched singular systems (SSSs) are investigated.
• The input-to-state stability (ISS) problems for discrete-time nonlinear SSSs are concerned.
• The ISS criteria are obtained via average dwell time approach and iterative algorithm of discrete-time systems.
• The switching rules are optimized and designed.

This paper investigates the input-to-state stability (ISS) problems for a class of discrete-time nonlinear switched singular systems (SSSs). Two novel ISS criteria are proposed based on average dwell time (ADT) approach and iterative algorithm of discrete-time systems (IADS). In particular, the following two cases are considered for the underlying systems: the first case is that all the sub-systems are exponentially stable, and the other case is that only a few sub-systems are exponentially stable. The corresponding ISS criteria are obtained to guarantee that the closed-loop systems are input-to-state stable via ADT approach and IADS. We neither construct a specific Lyapunov function for ISS in the proof process of the stability criteria nor design a specific structure of the control inputs. The design deficit of the switching controllers is optimized and the design difficulty of the switching controllers is reduced via the proposed criteria. Finally, two numerical examples are provided to illustrate the feasibility of the results obtained.