Abstract-This paper presents a sum of squares (SOS) approach to the stability analysis of networked control systems (NCSs) incorporating time-varying delays and time-varying transmission intervals. We will provide mathematical models that describe these NCSs and transform them into suitable hybrid systems formulations. Based on these hybrid systems formulations we construct Lyapunov functions using SOS techniques that can be solved using LMI-based computations. This leads to several advantages: (i) we can deal with nonlinear polynomial controllers and systems, (ii) we can allow for nonzero lower bounds on the delays and transmission intervals in contrast with various existing approaches, (iii) we allow more flexibility in the Lyapunov functions thereby possibly obtaining improved bounds for the delays and transmission intervals than existing results, and finally (iv) it provides an automated method to address stability analysis problems in NCS.

Abstract-This paper presents a sum of squares (SOS) approach to the stability analysis of networked control systems (NCSs) incorporating time-varying delays and time-varying transmission intervals. We will provide mathematical models that describe these NCSs and transform them into suitable hybrid systems formulations. Based on these hybrid systems formulations we construct Lyapunov functions using SOS techniques that can be solved using LMI-based computations. This leads to several advantages: (i) we can deal with nonlinear polynomial controllers and systems, (ii) we can allow for nonzero lower bounds on the delays and transmission intervals in contrast with various existing approaches, (iii) we allow more flexibility in the Lyapunov functions thereby possibly obtaining improved bounds for the delays and transmission intervals than existing results, and finally (iv) it provides an automated method to address stability analysis problems in NCS.

In this thesis we are concerned with the stability analysis and the design of stabilizing compensators for networked control systems (NCSs) that exhibit packet dropouts. We propose a new type of dropout compensator, depending on the local dropout history, for which we provide LMI-based synthesis conditions. The analysis and design framework includes both worst-case bound and stochastic models to describe the packet dropout behavior in both the sensor-to-controller and controller-to-actuator channel. Numerical examples demonstrate the significantly improved robustness with respect to packet dropouts using the proposed dropout compensator, compared to using the zero strategy and the hold strategy.

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Abstract-This paper provides an approach to analyze and design decentralized observer-based controllers for large-scale linear plants subject to network communication constraints and varying sampling intervals. Due to communication constraints, it is impossible to transmit all input and output data simultaneously over the communication network that connects sensors, actuators and controllers. A protocol orchestrates what data is sent over the network at each transmission instant. To handle these communication constraints, it is fruitful to adopt a switched observer structure that switches based on the transmitted information. By taking a discrete-time switched linear system perspective, we are able to derive a general model that captures all these aspects and provides insight into how they influence each other. Focusing on the class of so-called 'periodic protocols' (of which the well-known Round Robin protocol is a special case), we provide a method to assess robust stability using a polytopic overapproximation and LMI-based stability conditions. Although the design problem is in general non-convex, we provide a procedure to find stabilizing control laws by simplifying the control problem. The design of the controller exploits the periodicity of protocols and ignores the global coupling between subsystems of the plant and variation of the sampling intervals. To assess the robust stability of the resulting closed-loop system including the ignored effects, an a posteriori analysis is conducted based on the derived LMIs.