Control Of Positive Switched Systems Research Articles

Event-triggered Control of Positive Switched Systems with Actuator Saturation and Time-delay

This paper investigates the event-triggered control of positive switched systems with randomly occurring actuator saturation and time-delay, where the actuator saturation and time-delay obey different Bernoulli distributions. First, an event-triggering condition is constructed based on a 1-norm inequality. Under the presented event-triggering scheme, an interval estimation method is utilized to deal with the error term of the systems. Using a co-positive Lyapunov functional, the event-triggered controller and the cone attraction domain gain matrices are designed via matrix decomposition techniques. The positivity and stability of the resulting closed-loop systems are reached by guaranteeing the positivity of the lower bound of the systems and the stability of the upper bound of the systems, respectively. The proposed approach is developed for interval and polytopic uncertain systems, respectively. Finally, two examples are provided to illustrate the effectiveness of the theoretical findings.

Double Switchings Reliable Control of Positive Switched Systems With Unfixed Actuator Faults

This paper investigates the double switchings reliable control of positive switched systems with actuator faults. Different from existing fixed actuator faults, a class of unfixed actuator faults is introduced, where each subsystem can have several faults rather than only a fault. First, a periodic occurring fault is considered for the subsystems. Using linear Lyapunov functions with linear programming, a set of reliable controllers is designed for positive switched systems. Then, an average dwell time based switching law between the normal and faulty modes of subsystems is established. In detail, the considered systems consist of several switched subsystems, where the subsystems have normal and faulty modes. In such a case, two classes of multiple linear Lyapunov functions are constructed for the subsystems and the whole switched systems, respectively. Accordingly, two classes of reliable controllers are designed for the normal and faulty modes, respectively. Meanwhile, two classes of average dwell time switching laws, named double switchings laws, are designed for the subsystems and the whole switched systems, respectively. Finally, two examples are provided to illustrate the effectiveness of the proposed design.

Input-Output Finite-Time Control of Positive Switched Systems with Time-Varying and Distributed Delays

The problem of input-output finite-time control of positive switched systems with time-varying and distributed delays is considered in this paper. Firstly, the definition of input-output finite-time stability is extended to positive switched systems with time-varying and distributed delays, and the proof of the positivity of such systems is also given. Then, by constructing multiple linear copositive Lyapunov functions and using the mode-dependent average dwell time (MDADT) approach, a state feedback controller is designed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is input-output finite-time stable (IO-FTS). Such conditions can be easily solved by linear programming. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

Finite-Timel1-Gain Control for Positive Switched Systems with Time-Varying Delay via Delta Operator Approach

This paper is concerned with the problem of finite-timel1-gain control for positive switched systems with time-varying delay via delta operator approach. Firstly, sufficient conditions which can guarantee thel1-gain finite-time boundedness of the underlying system are given by using the average dwell time approach and constructing an appropriate copositive type Lyapunov-Krasovskii functional in delta domain. Moreover, the obtained conditions can unify some previously suggested relevant results seen in literature of both continuous and discrete systems into the delta operator framework. Then, based on the results obtained, a state feedback controller is designed to ensure that the resulting closed-loop system is finite-time bounded with anl1-gain performance. Finally, a numerical example is presented to demonstrate the effectiveness and feasibility of the proposed method.

Stability and -Gain Control of Positive Switched Systems with Time-Varying Delays via Delta Operator Approach

This paper investigates the problems of stability and <svg style="vertical-align:-3.27605pt;width:12.15px;" id="M2" height="17.424999" version="1.1" viewBox="0 0 12.15 17.424999" width="12.15" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.625,12.725)"><use xlink:href="#x1D459"/></g> <g transform="matrix(.012,-0,0,-.012,5.2,16.8)"><use xlink:href="#x31"/></g> </svg>-gain controller design for positive switched systems with time-varying delays via delta operator approach. The purpose is to design a switching signal and a state feedback controller such that the resulting closed-loop system is exponentially stable with <svg style="vertical-align:-3.27605pt;width:12.15px;" id="M3" height="17.424999" version="1.1" viewBox="0 0 12.15 17.424999" width="12.15" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.625,12.725)"><use xlink:href="#x1D459"/></g> <g transform="matrix(.012,-0,0,-.012,5.2,16.8)"><use xlink:href="#x31"/></g> </svg>-gain performance. Based on the average dwell time approach, a sufficient condition for the existence of an <svg style="vertical-align:-3.27605pt;width:12.15px;" id="M4" height="17.424999" version="1.1" viewBox="0 0 12.15 17.424999" width="12.15" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.625,12.725)"><use xlink:href="#x1D459"/></g> <g transform="matrix(.012,-0,0,-.012,5.2,16.8)"><use xlink:href="#x31"/></g> </svg>-gain controller for the considered system is established by constructing an appropriate copositive type Lyapunov-Krasovskii functional in delta domain. Moreover, the obtained conditions can unify some previously suggested relevant methods in the literature of both continuous- and discrete-time systems into the delta operator framework. Finally, a numerical example is presented to explicitly demonstrate the effectiveness and feasibility of the proposed method.