Research On Structural Properties Of Systems

Structural properties of systems, such as structural controllability, structural observability etc., are more general descriptions of system features, which imply the influence and effect of parameters on systems. The resultes obtained by structural property research have some theoretical meaning on analysis the effect of chosed parameters for systems. Especially on the production process, these conclusions have pratical meaning. Taking the different values in parameter space, the properties of some certain system may change, such as structural controllability, structural observability, because the independent parameters of systems can imply the structural properties entirely, which can be regarded as the third parameter inaddtion to system state and system input.The properties obtained from the field of real numbers show us that when there are unknown parameters or system parameters changed by disturbance (the parameters which are unknown or may be changed are defined as system parameters), these properties over the field of real numbers are not suitable. So it is important to explore the properties of systems which contain parameters.The main work of this dissertation is that extend the structural properties of linear systems to that of nonlinear systems, that is, research the structural controllability, structural observability and reducibility. These structural properties of nonlinear systems can imply that there is not any (almost no) influence and effect of parameters on systems also, so chosing the parameters in parameter space when analyze the dynamic process of nonlinear systems is not important, and the main work when designing is how to chose some parameters to satisfy the system properties. All the conclusions shown in this dissertation are based on differential geometric and polynomial theory respectively. Althouth the mathematic tools are different, for the same system, we can get the same result, which show the correctness of these conclusions.The main conclusions are as follows:(1) The nonlinear system is said to be locally weak structural controllable at some points x0, if the nonlinear system satisfy the structural controllability Lie condition at x0;(2) The nonlinear system is said to be weak structural controllable, if this system is locally weak structural controllable;(3) For the SISO nonlinear system, it is said to be structural controllable if and only if numerator and denominator of its transfer function have no common left divisor;(4) The nonlinear system is said to be locally weak structural observable at some points x0, if the nonlinear system satisfy the structural observability Lie condition at x0.In addition, we also make some research on structural reducibility of nonlinear systems, and show that if the nonlinear system described by polynomial is structural reducible it must not have the autonomous variable. For the composite nonlinear systems we make some preliminary study. Because we use the noncommutative algebraic theory the conclusions obtained are to some extent different from that for linear systems in frequence domain. The main difference is of noncommutation. The identifiability of parameters is reseached when we make the study on structural observability, and show that for the unidentifiability of parameters the states may be not identifiable which result in the unobservability of system.Last, for linear active RLCM network we discuss the structural properties of coefficient matrices of state eqution and output equation. With the help of using the conclusions on structural controllability and observability of passive networks over F(z), we get the conditions on structural controllability and observability of active RLCM networks. These conditions provides the theoretical methods on which we can design an active RLCM network to be a structural controllable, observable and stable active network, and we can conveniently design and apply the active RLCM netwoks.