Controller And Filter Of Positive Systems With State Saturation Based On Event-triggered Mechanism

In the real world,there exists a class of systems that can be used to model dynamic processes with non-negative variables.This kind of systems is called positive systems.Positive systems are widely used in practice such as formation flying systems in the air,virus mutation research in biomedical systems,queuing systems,and so on.Due to aging or performance damage of components,the state of the system is often subject to saturation.Most of literature only consider input saturation/actuator saturation constraints,but they ignore the influences of state saturation on the systems.Meanwhile,the signal sampling mechanism in the literature is mainly based on the periodic time-triggered sampling mechanism.Such a sampling mechanism easily leads to the waste of resources.In some control systems such as network communication systems,the time-triggered mechanism is impractical owing to the limited bandwidth and heavy burden of communication networks.Thus,the event-triggered sampling mechanism is introduced to deal with these problems.For the synthesis of systems,controller and filter are two basic and important research topics.This thesis mainly studies the event-triggered controller and filter design of positive systems with state saturation.The specific contents are as follows:Chapter 1 first introduces the research background and significance of this thesis.Then,the research status of positive systems and switched positive systems are summarized.Furthermore,the event-triggered controller and filter design of positive systems are introduced.Finally,the main research of this thesis is summarized.Chapter 2 studies the saturation control problem of positive systems based on eventtriggered mechanism.First,an event-triggering condition based on a 1-norm is established for positive systems subject to input saturation.By virtue of linear copositive Lyapunov functions and linear programming approach,the event-triggered controller is designed to ensure the positivity and stability of the systems.For positive systems with state saturation constraints,the original systems are transformed into interval uncertain systems using the method of matrix decomposition.Furthermore,the positivity and stability of the original systems can be transformed to research the stability and stability of the upper bound of the interval uncertain systems.All the proposed conditions are solvable in terms of linear programming.Finally,the proposed approaches are extended to continuous-time positive systems.Chapter 3 proposes the event-triggered control of positive systems with state saturation.First,an event-triggering condition in the form of 1-norm is established based on the relationship between error and measurable output.Under the presented event-triggering condition,the filter system is transformed into an interval uncertain system.Using a linear copositive Lyapunov function,an l1-gain filter is designed for the systems subject to exogenous disturbance.Finally,two types of non-fragile filter frameworks involving additive and multiplicative perturbations are proposed.A cone invariant set is constructed to ensure that the state of the filter systems can be maintained in it.Chapter 4 designs a class of event-triggered filters for switched positive systems with state saturation constraints.First,the event-triggering condition in the form of 1-norm is used to transform the filter system into an interval uncertain system.Furthermore,the positivity and error dynamics of the filter system are obtained through the lower bound of the interval system.By constructing multiple linear copositive Lyapunov functions,the stability of the filter system is obtained through the lower bound of the interval uncertain system.Finally,two kinds of matrix decomposition approaches are introduced to design the filter gain matrices.Two classes of non-fragile filter frameworks including additive and multiplicative fluctuations are established for switched positive systems.Chapter 5 sums up the research contents and puts forward some further issues.