Discrete-time Subsystem Research Articles

Necessary and sufficient conditions for quadratic stabilizability of switched systems on non-uniform time domains

In this paper, we consider the quadratic stabilizability via state feedback for a particular class of switched systems that evolve on a non-uniform time domain by introducing time scales theory. The system considered switches between a continuous-time subsystem with variable lengths and a discrete-time subsystem with variable discrete step sizes. Necessary and sufficient conditions are derived to guarantee the quadratic stability of this class of switched systems via a switching state feedback law based on the existence of a common positive definite matrix satisfying the quadratic stabilizability condition by considering that the two subsystems are unstable. By state feedback, we mean that the switching among subsystems depends on the system states. Current results for this kind of state switching feedback control are derived only for switched systems evolving on a continuous time domain or a discrete time domain with fixed step’s size. These results are not applicable for the particular class of switched systems where there is a mixing between the continuous and discrete dynamics. This motivates the derivation of a new and more general state feedback control law for switched systems in this work. A numerical example illustrating the results is presented.

Second-Order Consensus for Multiagent Systems With Switched Dynamics and Sampled Position Data

This article studies the consensus control problem of second-order multiagent systems with switching dynamics, which consist of a continuous-time and a discrete-time subsystem. A novel control protocol is proposed for fixed digraphs by using the same control strategy for two subsystems so that the controller can keep the control strategy unchanged when systems switch. Moreover, this control strategy uses only sampled position data at the current sampling time and the previous sampling time to deal with this possible situation when speed information is difficult to be measured, which is also robustness and low cost. Some necessary and sufficient conditions to achieve consensus are derived about the network topology, structure and sampling period. At last, a few simulation examples are given.

A dwell time approach for the stabilization of mixed Continuous/Discrete switched systems

In this paper, we study the stabilization properties of Continuous/Discrete switched systems using the dwell time approaches. The considered system switches between a continuous-time subsystem evolving on time intervals with variable lengths and a discrete-time subsystem with variable discrete step sizes. Since the time domain is non-uniform, and the stability of the discrete-time subsystem with variable discrete step sizes does not depend only on the dynamic of the system, but also on the length of the discrete steps, the usual conditions of dwell time approaches may not be applicable to stabilize this special class of switched systems. Motivated by that, stabilizing dwell time and average dwell time conditions are derived by introducing the time scales theory and numerical examples are proposed to illustrate the effectiveness of the proposed methods.

Interval consensus of switched multiagent systems

This paper studies interval consensus for switched multiagent systems over directed networks, which consist of a continuous-time subsystem and a discrete-time subsystem regulated by a switching rule. Interval consensus refers to a state constrained consensus, where each agent is allowed to propose an acceptable interval to saturate their expressed states and the final consensus state lies in the nonempty intersection of all these intervals. We establish conditions guaranteeing interval consensus for switched multiagent system under arbitrary switching rules. Furthermore, we introduce the scaled interval consensus notion, which allows both the convergence of states to a pre-assigned proportion and the scaled consensus values lying in the desired range. Simulation results are provided to verify the effectiveness of the theoretical results.

Second-Order Consensus for Multiagent Systems With Switched Dynamics.

This article investigates the consensus control problem for second-order multiagent systems with switched dynamics, consisting of a continuous-time subsystem and a discrete-time subsystem. Under a fixed directed topology, two linear control protocols are proposed for achieving consensus. One is that two subsystems use different control inputs, where the continuous-time system uses continuous-time control, and the discrete-time system uses discrete-time control. In order to reach consensus for this kind of control protocol, some necessary and sufficient conditions are derived. The other is to use the same control algorithm for the two subsystems, which is a sampled-data control input. Similar consensus conditions are also obtained. Finally, a few simulation examples are given to verify the theoretical results.

Event-triggered control for switched systems with both continuous-time and discrete-time subsystems

ABSTRACTIn this paper, we consider the event-triggered control for a class of switched systems which are composed of one continuous-time subsystem and one discrete-time subsystem. The proposed event-triggered mechanism adopts the form of periodic triggering, which combines the advantages of periodic control and event-triggered control. Consequently, Zeno behaviour can be essentially eliminated. A criterion is presented to ensure the exponential stability of the closed-loop switched systems. In addition, we extend the above result to the case of the switched system with multiple continuous-time and discrete-time subsystems and the case of observer-based control. Finally, a numerical example is provided to illustrate the theoretical results.

Stability of Wide-Area Power System Controls With Intermittent Information Transmission

This paper investigates the stability problem of wide-area damping controllers with intermittent information transmission. Due to the interruption in communication links between remote measurements and damping controller or from the damping controller to the damping actuators, the closed-loop system might become unstable. The instability is strongly related to the duration of interruption of information transmission. To estimate instability, this paper formulates the problem as continuous/discrete-time switched system and the stability conditions are derived using time-scale theory. This method allows us to handle continuous and discrete dynamics as two pieces of the same framework, such that the system will switch between a continuous-time subsystem (when the communication occurs without any interruption) and a discrete-time subsystem (when the communication fails). The contribution is to estimate the maximum allowable value of the time of interruption of information transmission that does not violate the exponential stability of the closed-loop system. The findings are useful in specifying the minimum requirements for communication infrastructure and the time to activate remedial action schemes. Simulations are performed based on both linear and nonlinear systems to validate the theoretical development.

Stability analysis of a class of switched nonlinear systems using the time scale theory

This paper investigates stability for a class of switched nonlinear systems evolving on a non-uniform time domain. The studied class of systems switch between a nonlinear continuous-time and a nonlinear discrete-time subsystem. This problem is formulated using time scale theory where the latter is formed by a union of disjoint intervals with variable lengths and variable gaps. Using Gronwall’s inequality and properties of the time scale exponential function, sufficient conditions are derived to ensure exponential stability. The results can be applied to cases where the continuous-time subsystem or the discrete-time subsystem is not necessarily stable, and the state matrices of each subsystem are not necessarily pairwise commuting. To illustrate the effectiveness of the proposed scheme, the consensus problem for general linear multi-agent systems under intermittent information transmissions is studied under this framework.

Containment Control for General Second-Order Multiagent Systems With Switched Dynamics.

This paper investigates the distributed containment control problem for a class of general second-order multiagent systems with switched dynamics, which is composed of a continuous-time (CT) subsystem and a discrete-time (DT) subsystem. For this switched multiagent system under fixed directed topology, a distributed containment control protocol is proposed for each follower based on the relative local measurements of neighboring followers and leaders. Some necessary and sufficient conditions are derived under the condition that the network topology contains a directed spanning forest, and these conditions ensure that the general second-order containment control problem can be solved under arbitrary CT-DT switching. If the general second-order system is reduced to the double integrator system, some simpler containment conditions are presented. Furthermore, the similar results are also obtained under switching directed topology. Finally, some simulation examples are presented to show the efficiency of the theoretical results.

Stability of switched systems on non-uniform time domains with non commuting matrices

The time scale theory is introduced to study the stability of a class of switched linear systems on non-uniform time domains, where the dynamical system commutes between a continuous-time linear subsystem and a discrete-time linear subsystem during a certain period of time. Without assuming that matrices are pairwise commuting, some conditions are derived to guarantee the exponential stability of the switched system by considering that the continuous-time subsystem is stable and the discrete-time subsystem can be stable or unstable. Some examples show the effectiveness of the proposed scheme.

Stability analysis of a class of uncertain switched systems on time scale using Lyapunov functions

This paper deals with the stability analysis of a class of uncertain switched systems on non-uniform time domains. The considered class consists of dynamical systems which commute between an uncertain continuous-time subsystem and an uncertain discrete-time subsystem during a certain period of time. The theory of dynamic equations on time scale is used to study the stability of these systems on non-uniform time domains formed by a union of disjoint intervals with variable length and variable gap. Using the concept of common Lyapunov function, sufficient conditions are derived to guarantee the asymptotic stability of this class of systems on time scale with bounded graininess function. The proposed scheme is used to study the leader–follower consensus problem under intermittent information transmissions.

Sampled-data control of networked linear control systems

In this paper, the problem of synthesis and analysis for the networked control systems (NCSs) with time-driven digital controllers and event-driven holders is considered. The NCS is modelled as a sampled-data system with time-delay in its discrete-time subsystem. This model is able to capture many network-induced features, for example, time-delay and packet dropout. Moreover, the model allows different combinations of the time-driven or event-driven mode of the devices, including the samplers, the controllers and the holders. By transforming time-delay in the discrete-time subsystem into its continuous-time subsystem of the sampled-data system, we have also obtained a less conservative time-delay dependent stability result for the NCSs, using a new Lyapunov function and a relaxed condition. Some limitations of the existing literatures on network-induced time-delay and sampling period are removed in the proposed framework. Furthermore, a sampled-data control design procedure is developed for the NCSs. Linear matrix inequality approach has been employed to solve the stability and control design problems. Finally, numerical examples are included to demonstrate the effectiveness of the proposed stability result and the potential of the proposed techniques.

Discussion on: “Stabilization of Networked Control System with Time Delays and Data-packet Losses”

In this paper, the problem of synthesis and analysis for the networked control systems (NCSs) with time-driven digital controllers and event-driven holders is considered. The NCS is modelled as a sampled-data system with time-delay in its discrete-time subsystem. This model is able to capture many network-induced features, for example, time-delay and packet dropout. Moreover, the model allows different combinations of the time-driven or event-driven mode of the devices, including the samplers, the controllers and the holders. By transforming time-delay in the discrete-time subsystem into its continuous-time subsystem of the sampled-data system, we have also obtained a less conservative time-delay dependent stability result for the NCSs, using a new Lyapunov function and a relaxed condition. Some limitations of the existing literatures on network-induced time-delay and sampling period are removed in the proposed framework. Furthermore, a sampled-data control design procedure is developed for the NCSs. Linear matrix inequality approach has been employed to solve the stability and control design problems. Finally, numerical examples are included to demonstrate the effectiveness of the proposed stability result and the potential of the proposed techniques.