Input-to-state stability analysis for a class of nonlinear switched descriptor systems

Abstract

This paper considers the problem of input-to-state stability for a class of nonlinear switched descriptor systems. According to the definition of input-to-state stability, sufficient conditions are derived to ensure that the system is input-to-state stable based on the dwell time approach and the Gronwall-Bellman inequality. Compared with existing methods, it is more convenient to design the controller for each subsystem, because it does not need to construct the input-to-state stable control Lyapunov function and design the specific structure of the control inputs. Finally, two numerical examples illustrate the feasibility and effectiveness of the proposed method.

Non‐fragile sliding mode control of discrete switched singular systems with time‐varying delays

“…When the differential equation (or difference equation) in a singular system is composed of switched subsystems, the singular system is developed into a switched singular system [23–28]. So far, switched singular systems are widely applied to practical systems like coupled networks and boost or buck converters [29–31]. It is worth mentioning that one obvious difference between singular switched systems and regular switched ones is that the instantaneous state jumps in former systems cannot be avoided, even if each subsystem is impulse‐free (or causal) and regular.…”

Input and output strictly passive $$H_\infty $$ control of continuous switched singular systems

“…It is difficult to eliminate state jumps using simple proportional state feedback (PSF). Many results on stability were achieved under an assumption that states do not jump at switching instants (see Gao et al 2015;Yang et al 2014;Zamani and Shafiee 2014;Zamani et al 2015). (2) Impulse behavior often occurs in some singular subsystems, which may cause the whole system to be unstable.…”

Robust nonfragile observer‐based control of switched discrete singular systems with time‐varying delays: A sliding mode control design

“…When all or some of the subsystems contain singular perturbation, the switched system is developed into a switched singular system. Such systems are widely used in practical systems including networked control systems, boost, or buck converters . It is noted that the stability, stabilization, and control issues for such systems are more complex than normal ones because the state consistence under switching between subsystems, regularity, impulse elimination (or causality), and stability are under consideration at the same time.…”