Dissipativity-Based Control And Filtering For Complex2-D Systems

With the informationize and networking of society,the complexity of actual system and signal is increasing.More and more systems are characterized by multiple variables and multiple dimensions.Therefore,the multi-dimensional system theory has become a research hotspot of control theory.As a typical multi-dimensional system,two-dimensional(2-D)system has the characteristic of updating information along two(horizontal and vertical)dimensions,and it has been successfully applied in electric power system,batch process control,metal rolling process control,multi-dimensional digital image comprehensive processing and vehicle/aircraft queue control.The deep and extensive engineering physics background makes 2-D system occupy a very important position in the control theory.As is well known,the stability is one of the most fundamental problems in control theory and application.Compared with the stability,dissipativity is a more important and general system performance.Dissipativity was first introduced by Willems in 1972.Dissipative theory is an idea that designs control system with an input-output energy-related characterization.It is also a new method of stability analysis of the system.On the one hand,the structure changes or sudden faults,which can be represented as the switched system,often occur to practical system.On the other hand,engineering systems usually operate in a designated finite-region,which makes it important to study the system performance in a finite-region.However,many established results for conventional one-dimensional(1-D)systems have not been extended to 2-D systems due to their multi-dimensional properties and structural complexity.In summary,the problems of dissipative control and filtering for 2-D switched systems and finite-region dissipative control for 2-D continuous-discrete systems are studied in this paper by combining the theories of 2-D systems and dissipativity.The core contents of this paper are as follows:(1)Based on the Fornasini Marchesini(FM)state space model,the dissipative control problem of 2-D switched systems is considered.Firstly,combining the theories of 2-D systems,switched systems and dissipativity,sufficient conditions are developed to guarantee that the system is asymptotically stable under the arbitrary switching signal case and exponentially stable under the restricted switching signal case with the dissipativity.Simultaneously,the mathematical methods,such as Lyapunov function,iterative formula,matrix technique,inequality technique and extended average dwell time are used.Secondly,based on the obtained dissipative stability conditions of 2-D switched systems,2-D(T,S,R)-g-dissipative state feedback controller design problem is solved by using LMI method.Finally,the effectiveness of the proposed design method is illustrated by an example of thermal process.(2)Based on the FM state space model,the dissipative filter design problem of 2-D switched systems is studied.In Chapter 3,the dissipative stability conditions of 2-D switched systems is given.In this chapter,based on the obtained dissipative stability conditions of 2-D switched systems,sufficient conditions are derived to guarantee that the filtering error system is asymptotically stable under the arbitrary switching signal case and exponentially stable under the restricted switching signal case with the dissipativity.Further,the desired 2-D(T,S,R)-9-dissipative filter is designed via applying the decoupling technology and LMI method.Finally,a simulation example is given to verify the correctness of the filter design method.(3)The problem of finite-region dissipativity-based control for a class of 2-D continuous-discrete systems is addressed.First of all,combining 2-D systems theory and dissipativity theory,sufficient conditions ensuring the finite-region boundedness and finite-region(T,S,R)-?-dissipativity are derived by utilizing the mathematical methods such as Lyapunov function,mathematical induction,iterative formula,matrix technique and inequality technique.Then,based on the obtained finite-region(T,S,R)-?-dissipativity conditions,the desired observer-based state feedback controller is designed.Finally,the dissipativity of the designed controller is verified by a numerical simulation.