Font Size: a A A

Stability Analysis And Stabilization Design For Linear Switched Positive Systems

Posted on:2018-11-05Degree:MasterType:Thesis
Country:ChinaCandidate:S X FengFull Text:PDF
GTID:2428330572465524Subject:Control theory and control engineering
Abstract/Summary:PDF Full Text Request
As a special class of hybrid systems,switched systems consist of a family of subsystems and a switching rule orchestrating the switching among the subsystems.Positive systems are a class of systems whose state is nonnegative for any nonnegative initial state.Switched positive systems are switched systems whose subsystems are positive systems.Such kinds of systems have extensive applications in the control of network congestion,formation flying and infections disease.This thesis studies linear switched positive systems focusing on stability analysis and stabilization design.The main contents of this thesis are as follows:Firstly,this thesis is concerned with the stability and robust stability of continuous and discrete linear switched positive systems whose subsystems are all unstable.The main idea is to design the appropriate switching behaviors to compensate the state divergence made by unstable modes.By this way,we can derive the asymptotic stability of the linear switched positive systems.By means of the mode-dependent dwell time approach and a class of discretized co-positive Lyapunov functions,a stability condition of linear switched positive systems with all modes unstable is derived.The co-positive Lyapunov functions constructed in this paper are time-varying during the dwell time and time-invariant afterwards.Moreover,the mode-dependent dwell time is required to confined by a pair of upper and lower bounds to guarantee the asymptotic stability.At the same time,the above approach is extended to the interval switched positive systems.Secondly,this thesis investigates the problem of asynchronous reliable control for a class of linear impulsive switched positive systems with actuator failures.The asynchronous switching means that the switching instants of the controller exceed or lag behind those of the systems.At the same time,in practical engineering systems,there inevitably exist actuators failures.By using the average dwell time approach and multiple linear co-positive Lyapunov functions,sufficient conditions in terms of LMIs for the exponential stability of the closed-loop linear impulsive switched positive systems with actuator failures are presented.Moreover,a set of state feedback reliable controllers for the stability of the closed-loop systems are constructed.Finally,this thesis investigates the problem of weighted L1-gain performance of the linear impulsive switched positive systems with the asynchronous switching and actuator failures.Due to the abrapt jumps at switching instants during the dynamical process,the state of the systems is discontinuous,and thus the process of the study is more complicated.By using the average dwell time approach,we derive the sufficient conditions for the expected weighted L1-gain performance of the systems.A numerical example is given to illustrate the effectiveness of the proposed method.
Keywords/Search Tags:Linear switched positive systems, Stability, Dwell time, Asynchronous switching, Actuator failures
PDF Full Text Request
Related items