A Study On Integrity Conditions And Design Of Controllers With Integritybased On LMI Approach

The aim of integrity control is to design controllers for MIMO systems so thatthe closed-loop control system can maintain stability and reach a good performanceagainst sensor/actuator failures. Since sensors are components that fail mostfrequently in a real control system, integrity control is of high value in applicationand widely investigated in recent years. Discussed in this thesis are integrity conditions of linear MIMO systems anddesign procedures of controllers with integrity. A [0,σ] failure model is used inmost sections to represent the on-off, attenuation or amplification in feedbackchannels, while dynamic output-feedback control law is applied to avoid the difficultyof obtaining the states of the system. The problems studied in this thesis are as follows: 1. Integrity conditions of linear time-invariant (LTI) systems in frequencydomain are derived by using the conditions of robust stabilization of normalizedcoprime factor plant descriptions, and the conditions can be used to analyze theintegrity of the system. 2. Integrity conditions and design procedures of controllers with integrity forLTI systems with no disturbances on parameters are proposed based on a linearmatrix inequality (LMI) approach. Controllers can be obtained easily and quickly bysolving two matrix inequalities. The number of parameters to be adjusted during thedesign process is less than that with Riccati method and the parameterization ofcontrollers is also given by the integrity conditions. 3. Robust integrity conditions and design procedures of controllers withintegrity for LTI systems with additive disturbances on parameters are proposedbased on an LMI approach. Under these conditions, the closed-loop system can be notonly stable against sensor/actuator failures but also robust with respect to parameteruncertainties. 4. Integrity conditions and design procedures of controllers with integrity andpole-constraints for LTI systems with no disturbances on parameters are proposedbased on an LMI approach. Under these conditions, the closed-loop poles are located IIin a specified region of left half plane so that the system can maintain good dynamicand static performances. 5. Integrity conditions and design procedures of controllers with integrity forLTI time-delay systems with no disturbances or additive disturbances on parametersare proposed based on an LMI approach. Under these conditions, the closed-loopsystem is stable against any time-delay, and robust to parameter uncertainties. The problems to be further studied are to reduce the conservativeness of theseintegrity conditions and optimize the design parameters during the design process. The effectiveness of the theorems and design procedures are all demonstratedby numerical examples.