Saturation Control Of Linear Systems Analysis

The saturation characteristic widely exists in almost all kinds of control systems, suchas actuator saturation or artificially added amplitude limiters for safe reasons. Its existence(or involvement) may change originally linear systems to nonlinear ones, so the systems'characteristic is changed. Profound influence to systems by reason of actuator saturation isdue to the fact that the command control is different from that actually accepted by plant.Extremely, the system is out of control of the command as deep saturation occurs.The topic of this thesis comes from the project named Constrained Control Problemsin Complex Systems supported by National Natural Science Foundation of China. Its aim isto carry on dynamic analysis for linear systems with actuator saturation. The systemsinvolved include continuous and discrete time, certain and uncertain, single-variable andmultivariable. The thesis is primarily focused on stability analysis, but also on the L₂ gainanalysis from system disturbance to output. The research work is based on Lyapunovstability theory, and adopts saturation degree method and H-matrix (or convex combined)method to deal with actuator saturation. All the calculations are mainly based on matrixeigenvalue and linear matrix inequality (LMI).By means of the saturation degree method, the thesis gets a sufficient condition (orcriterion) to test whether a single-variable linear continuous-time system with saturatedstate feedback is globally asymptotically stable (GAS) or regionally asymptotically stable(RAS), meanwhile, suggests an algorithm to estimate an invariant attraction (super)ellipsoid for the latter case, also gets the corresponding results for the systems with outputfeedback plus a state observer. Making use of H-matrix method for multivariable linearcontinuous-time systems with saturated state feedback, the thesis transforms the estimateproblem of L₂ gain from disturbance to output into an optimization problem with LMIconstraints, and obtains the smallest L₂ gain estimate under optimization support. Based onHu's work on actuator saturated discrete-time systems (ASDTS), the thesis analyzes thesystem stability and L₂ gain for parameter-dependent systems (PDS) by means of H-matrixmethod. The Lyapunov function candidates include three kinds, they are: (ⅰ) independent (ⅱ)only parameter dependent (ⅲ) both parameter and saturation dependent. Conservativenessof the results reduces in turn, and forgiveness increases in turn. Solving correspondingoptimization problems gives the smallest gain estimate in cases of (ⅰ)-(ⅲ), meanwhile, thecalculating conservativeness reduces in turn.The results are all attached with corresponding algorithms and confirmed withexamples.