Robust Finite-Time Filtering And State Estimation Of Switched Control Systems

Modern control systems are becoming progressively complex and it may not be feasible to formulate overall system only as continuous variable dynamical system or discrete event dynamic system. Several real-world systems are inherently hybrid because of the presence of multiple dynamics in the system. Switching systems are a distinct subclass of Hybrid systems modeled by unfussy mathematical structure and are composed of multiple subsystems or modes. Interaction between these modes is governed by a piecewise constant deterministic switching signal. Stability of switching system is not trivial because overall switching system can be unstable even if all subsystems are asymptotically stable. Additionally, for a switching system with one or more (or all) unstable subsystem modes, it is possible to construct a switching law or switching signal such that the overall switching system dynamics exhibit stable and bounded behavior. Many variations of Lyapunov function are used to address this stability issue.The traditional concepts of Lyapunov asymptotic stability play a dominate role in control domain; however, in a practical consideration, the extent of asymptotic stability may not be clear. The concept of so called Practical Stability defines the extent of asymptotic stability for real-world applications. Finite time stability theory deals with a finite interval of time in addition to prescribed bounded values for system variables similar to the concept of Practical stability. The conception of Finite-Time Stability is important from multiple aspects. Real-world systems are apparently supposed to run for a finite time interval. In addition, for systems operating at infinite or long time, in many cases, only a short time interval is important and subject to stability problems e.g. saturation, overshoot, fault occurrence etc. Finite-time stability theory for dynamical systems in the presence of external disturbance leads to the concept of finite-time boundedness. These conceptions have gained much attention of the researchers particularly after the emergent utilization of linear matrix inequalities in the field of control systems.Filtering and state estimation procedures fulfilling H∞performance index are vital for robust control system design. This dissertation work proposes new results and synthesis procedures for robust filtering and state estimation of switched control systems in the framework of finite-time stability, which can be briefly mentioned as:4Robust filtering problem has been explored and new design procedures have been proposed by implementing the Hχ performance criteria. The finite-time stability and boundedness criteria have been fully analyzed for discrete-time switching systems subject to energy-bounded disturbance and norm-bounded parameter uncertainties, considering time-dependent dwell-time switching. Parametric optimization algorithm has been devised to present the stated results in LMI form, which provides an effective means to numerically solve the filter design problem. Multiple numerical examples and a practical example concerning the rotational displacement of DC motor modeled as a switching system is investigated to demonstrate finite-time filter design procedure, and to validate our proposed results.Robust finite-time bounded observer design has been presented considering asynchronous switching between observer and physical system. Luenberger observers have long been used for reliable state estimation of control systems. In the case of switching systems, observer is assumed to switch synchronously with the system in most published literature. In practice, observer switching will lag behind physical system because of inherent delays in sensing and measurement mechanism. Hence observer design considering asynchronous switching is more significant from practical view point. In our investigation we demonstrate finite-time switching observer design procedure both for synchronous and asynchronous cases, and follow H∞performance criteria for robust state estimation of discrete-time switching systems. Proposed results are validated by several design examples.Most of the existing switching system literature considers time-invariant systems. In this thesis work, new results are also presented demonstrating design steps for asymptotic and finite-time switching observer for time-varying polytopic uncertain switching systems. The innovative conception of parameter-dependent switched Lyapunov function has been exploited to investigate polytopic uncertain switching systems under classical Lyapunov asymptotic stability as well as finite-time stability criteria. A spring-mass-damper system is modeled as a polytopic uncertain switching system, and design steps are explained for designating parameter-dependent observer gains, along with additional numerical examples.