Stability analysis of nonlinear impulsive switched positive systems

In this paper, the global asymptotic stability (GAS) of continuous-time and discrete-time nonlinear impulsive switched positive systems (NISPS) are studied. For continuous-time and discrete-time NISPS, switching signals and impulse signals coexist. For both of these systems, using the multiple max-separable Lyapunov function method and average dwell-time (ADT) method, some sufficient conditions on GAS are given. Based on these, the GAS criteria are also given for continuous-time and discrete-time linear impulsive switched positive systems (LISPS). From our criteria, the stability of the systems can be judged directly from the characteristics of the system functions, switching signals and impulse signals of the systems. Finally, simulation examples verify the validity of the results.

Finite-Time Boundedness of Linear Uncertain Switched Positive Time-Varying Delay Systems with Finite-Time Unbounded Subsystems and Exogenous Disturbance

The problem of finite-time boundedness for a class of linear switched positive time-varying delay systems with interval uncertainties and exogenous disturbance is addressed. This characteristic research is that the studied systems include the finite-time bounded subsystems and finite-time unbounded subsystems. Both a slow mode-dependent average dwell time and a fast mode-dependent average dwell time switching techniques are utilized reasonably. And by applying a copositive Lyapunov-Krasovskii functional, novel delay-dependent sufficient criteria are derived to guarantee such systems to be finite-time bounded concerning the given parameters and designed switching signal. Furthermore, new finite-time boundedness criteria of the systems without interval uncertainties are also obtained. Finally, the efficiency of the theoretical results is presented in two illustrative examples.

Finite-time asynchronous control of discrete-time switched linear systems with event-triggered H∞ filtering

In this paper, the event-triggered H∞ filtering problem for discrete-time linear switched systems is investigated under asynchronous switching. Under the mode-dependent event-triggered transmission mechanism (METM), the switching signal and filtering signal are combined into an augmented switching signal by merging signal technology, and the switched system and filtering system are modeled as a filtering error system (FES). Because the switching signal of the filtering system is determined by METM, there will be an asynchronous switching phenomenon between the switched system and filtering system. The novel sufficient conditions are given to ensure that the FES is finite-time bounded (FTB) and has a specified H∞ performance by the average dwell time (ADT) and multi-Lyapunov functional method. And based on this, the design method of the H∞ filter is given. Ultimately, the numerical examples are inspired to manifest the availability of the effects in the study.

Observer-Based Control for Nonlinear Time-Delayed Asynchronously Switching Systems: A New LMI Approach

This paper designs an observer-based controller for switched systems (SSs) with nonlinear dynamics, exogenous disturbances, parametric uncertainties, and time-delay. Based on the multiple Lyapunov–Krasovskii and average dwell time (DT) approaches, some conditions are presented to ensure the robustness and investigate the effect of time-delay, uncertainties, and lag issues between switching times. The control parameters are determined through solving the established linear matrix inequalities (LMIs) under asynchronous switching. A novel LMI-based conditions are suggested to guarantee the H∞ performance. Finally, the accuracy of the designed observer-based controller is examined by simulations on practical case-study plants.

Sign Stability of Dual Switching Linear Continuous-Time Positive Systems

This paper investigates 1-moment exponential stability and exponential mean-square stability (EMS stability) under average dwell time (ADT) and the preset deterministic switching mechanism of dual switching linear continuous-time positive systems when a numerical realization does not exist. The signs of subsystem matrices, but not their structures of magnitude, are key information that causes a qualitative concept of stability called sign stability. Both 1-moment exponential stability and EMS stability, which are the traditional stability concepts, are generalized intrinsically. Hence, both 1-moment exponential sign stability and EMS sign stability are introduced and are proven based on sign equivalency. It is shown that they are symmetrically and qualitatively stable. Notably, the notion of stability can be checked quantitatively using some examples.

ISS and integral-ISS of switched systems with nonlinear supply functions

The problem of input-to-state stability (ISS) and its integral version (iISS) are considered for switched nonlinear systems with inputs, resets and possibly unstable subsystems. For the dissipation inequalities associated with the Lyapunov function of each subsystem, it is assumed that the supply functions, which characterize the decay rate and ISS/iISS gains of the subsystems, are nonlinear. The change in the value of Lyapunov functions at switching instants is described by a sum of growth and gain functions, which are also nonlinear. Using the notion of average dwell-time (ADT) to limit the number of switching instants on an interval, and the notion of average activation time (AAT) to limit the activation time for unstable systems, a formula relating ADT and AAT is derived to guarantee ISS/iISS of the switched system. Case studies of switched systems with saturating dynamics and switched bilinear systems are included for illustration of the results.

Event-triggered control of networked switched systems under network attacks

This paper is concerned with the event-triggered control (ETC) problem for switched systems in networked environments, which are suffered from denial-of-service (DoS) attack and deception attack. Considering that the packet in networked switched systems contains the sampled state and switching signal, DoS attack prevents the packet transmission to cause the zero input, while deception attack falsifies the packet to cause the asynchronous control input with nonlinear disturbance. First, the probabilistic characterization of invalid packet transmissions caused by two different attack models is constructed, namely the ratio of the number of packet transmissions suffering from network attacks to the total number of packet transmissions. Second, a suitable ETC scheme is designed to determine the next triggering instant, which guarantees that the value of Lyapunov function cannot exceed a given restriction and updates the control input at switching instant. After that, the average dwell time and control gains are designed to guarantee the almost sure asymptotic stability of such systems. Finally, a numerical simulation is given to verify the effectiveness of the theoretical results.