Stability and disturbance attenuation for linear switched systems

In this dissertation, methodologies for design and analysis of linear switched system that guarantee quadratic stability with disturbance attenuation levels will be considered. Techniques for design of stabilizing switching control logics and for analysis by constructing piecewise Lyapunov functions are developed, mostly based on the Bounded Real Lemma. These synthesis problems are further extended to take into account the effects of actuator limit bounds for an overall system performance by relying on the peak-to-peak gain minimization results. An important aspect of these techniques is that the problem can be reduced to a set of linear matrix inequalities that can be numerically solved by a variety of available softwares.; First, a full-state feedback design approach for a stabilizing switching control logic is presented such that it satisfies quadratic stability and L2 bound performance level. An output feedback switching controller with observer-based and general compensator structures are developed. These results are extended to a type of peak-to-peak minimization problem when the disturbance peak level is known. To further enhance the stability and performance level for switched systems a simultaneous design methodologies of a general compensator and stabilizing switching rule are proposed. A multi-objective approach was also formulated to take into account the saturation limits of the actuators. Numerical simulation results for the simultaneous approach indicate that there are significant improvements in the disturbance attenuation performance level compared to the results obtained by designing a controller and stabilizing switching rule separately.; An extension and implementation of the analysis technique by constructing a piecewise Lyapunov function is developed for linear switched system. This analysis method is extended to satisfy quadratic stability with some level of disturbance attenuation conditions. Simulation results show that a search for piecewise Lyapunov function can be successfully computed and the performance level improves with increasing number of partitions.; The main motivation here is to expand and apply this analysis approach by forming piecewise Lyapunov function for structural system with a single and multiple variable stiffness devices. Results illustrate that the analysis problem for structural system with a single device is simple and straight forward. For system with multi-states and multiple switching, it is geometrically constraining and challenging to solve using the basic analysis by piecewise Lyapunov function results. However, a systematic approach to the analysis problem is developed for structural system with multiple variable stiffness devices to resolve these geometric limitations. Due to the decentralized properties of these devices a linear transformation from device to state frame is utilized to set up and solve the analysis by constructing piecewise Lyapunov function problem. A comparison to passivity results indicate that the passivity method takes less effort to work out for the case when the system satisfy required passivity conditions. Nevertheless, the analysis results by forming piecewise Lyapunov function show that this technique can be effectively implemented for systems with multiple states and devices. This is a major contribution since it is the first effective implementation of the analysis method by piecewise Lyapunov function for multiple switched system with multi-states.; Lastly, using boundary layer principles a step-by-step procedure to design a modified hybrid switching control logic is develop to reduce chattering for switched systems. Chattering is a common problem and can be physically harmful for switched systems. The result establish that chattering is decreased by introducing boundary layers, while developing explicit trade-off measures for the size of boundary layer and guaranteed level of performance.