Analysis Of Steady-state Output Variance Range Of Stochastic Control Systems Based On BMI Method

A common performance index in stochastic control field is that the steady output variances (SOV) of the closed-loop system are less than a set of specified upper bounds. However, the SOV of the system are closely related to control structures and control strategies. So the analysis of the minimal SOV achieved by different structure controls is meaningful.In this paper, using the bilinear matrix inequalities (BMI) and linear matrix inequality (LMI), we study the minimal SOV achieved by three kinds of controls for a class of linear stochastic systems under constraints on the regional pole. Based on this, we can easily tell what kinds of output variance upper-bounds are feasible.The main content of this paper has three aspects as follows.1) Analysis of SOV achieved by static output feedback (SOF) under pole constraintsUsing the BMI, the mathematical model of the "minimal steady output variances" that can be achieved by SOF under constraint on poles is first given. Then, using path-following method solving BMI problem, an LMI based iteration algorithm is provided to find the approximate values of "minimal steady output variances" and the SOF matrix gains that realize these approximate-minimal steady output variances and pole constraints.2) Analysis of SOV achieved by observer-based feedback (OBF) under pole constraintsGeneralizing from SOF to OBF, a BMI model of the "minimal SOV" that can be achieved by OBF under constraint on poles is first given. Then, using path-following method to solve the corresponding BMI problem, an LMI based algorithm is provided to find the approximate values of "minimal steady output variances" and the corresponding observer matrices and feedback matrices which together realize these approximate-minimal steady output variances.3) Analysis of SOV achieved by dynamic output feedback (DOF) under pole constraintsFirst, DOF is changed to SOF of a generalized system. Then, an LMI iteration algorithm is provided to find the approximate values of "minimal SOV" and the corresponding DOF matrix gains.