Robust Analysis And Control For Uncertain Singularly Perturbed Systems

The two-time-scale decomposition technique is an essential method for dealing with continuous singularly perturbed systems.In general,these systems appear to be rigid and degenerate-somewhere for specific values-which rises challenging situation for the analysis and control problems.To clear out these complexities,the singular perturbation approaches was put forward,which have shown their effectiveness during the last four decades.Recent research on systems and control theory for singularly perturbed systems has been intense by its attraction toward many scholars.In this dissertation,we are mainly investigating robust stability and stabilization on disturbance,robust H?analysis and control for uncertain singularly perturbed systems with disturbance.Also the disturbance observer based control method is applied to a class of uncertain singularly perturbed systems with input nonlinearity.New results are obtained and new challenges have been noticed.The major works in this dissertation are summarized as follows:· Firstly,the problem of robust stability and stabilization on disturbance for uncertain singularly perturbed systems is studied via the concept of input-to-state stability.By using the fixed-point principle,we provide a linear matrix inequality sufficient condition to guarantee that the original system is in the standard form.Then,the reduction technique also known as the two-time scale decomposition is appealed to effectively decompose the system into slow and fast subsystems and made them input-to-state stable.Based on the ISSness of the limit system,a unified linear matrix inequality condition is presented to guarantee that the full order system is also input to-state-stable for all sufficiently small values of the perturbation parameter.In case where the unforced system is unstable,a control law is designed to make the closed-loop system in the standard form and robust input-to-state stable for ? sufficiently small.Later,the upper bound ?*is estimated in a new methodical and computational way.· Secondly,the H? analysis and control for singularly perturbed systems with disturbance and uncertainty appearing in all matrices components is tackled.By adopting the standard requirement for the system,the problem is solved via the concept of generalized quadratic stability and stabilizability.The H?performance analysis is systematically carried out for the limit system by providing necessary and sufficient conditions for the slow and fast subsystems to be generalized quadratically stable with an H? norm less than ?.Then a unified linear matrix inequality condition is given so that the original full order system is made generalized quadratically stable with an H? norm less than ? for ?sufficiently small.Thus the preservation of system's performance when ??0 and the generalized quadratic stability property are guaranteed for all adimissible parameter uncertainty.When unstablility happen,a controller is designed to make the closed loop system generalized quadratically stable with an H? norm less than ? for ? sufficiently small.The upper bound ?*is estimated by solving a generalized eigenvalue minimization problem.· Finally,the disturbance observer based control method is applied to a class of uncertain singularly perturbed systems with input nonlinearity.By choosing an appropriate Lyapunov storage function,the disturbance observer based control is designed so that the system is robustly stabilizable in one hande and robustly stabilizable with a prescribed performance level for ? sufficiently small in the oyher hand for all adimissible parameter uncertainty.For each case,a numerical example is given with simulations to show to effectiveness of the proposed methods and visualize the results.