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In this paper, a comparison of polytopic and norm-bounded approach is sought for stability analysis of networked control systems (NCS) with uncertain time-varying delays. The delays are considered to be general in the sense that these could be either smaller or greater than the sampling time. For stability analysis, first the continuous-time NCS plant is represented remodeled into an equivalent discrete time one. The uncertainties in the NCS model arises due to the time varying delays are modeled using both polytopic and norm-bounded approach. Considering a state-feedback controller, LMI conditions are used to exploit the stability region in the controller and delay parameter plane using two numerical examples. It is observed that the norm-bounded (NB) approach is slightly conservative whereas higher computational complexities are involved in the polytopic one.

this work is devoted to the analytic study of the characteristic roots of scalar autonomous Delay Differential Equations (DDEs) with complex coefficients. The focus is placed on the robust analysis of the position of the roots in C with respect to the variation of the coefficients, with the final aim of obtaining suitable representations for the relevant stability boundaries and charts. The investigation benefits from a preliminary shift of the coefficients which reduces the number of free parameters allowing for useful graphical visualizations. The present research is motivated on the base of studying the stability of systems of DDEs.

The purpose of this paper is to propose to the community involved in robust control theory studies a complete and meaningful, design and analysis problem to highlight theoretical as well as numerical issues pertaining to real life applications of sophisticated robust control design. This benchmark is based on the problem of attitude control of a flexible satellite developed at CNES. Linearized models of the dynamics, actuators and sensors are given with a sample of a possible control law. Finally, three different control design and analysis problems are defined to serve as guidelines for the evaluation of the proposed solutions

The static output feedback synthesis for LTI systems is considered. It is shown to have analogies with robust analysis, in particular the existence of an output feedback gain is equivalent to the existence of some quadratic separator. These considerations lead to formulate the problem as the synthesis of an ellipsoidal set of stabilising controllers. Based on this formulation important issues are developed for fragility, restricted controllers and also root-clustering.

For systems with parametric uncertainties, we propose a systematic method, based on the LQG form of any controller, to use the Parameter Robust Analysis by Bayesian Identification algorithm. It consists to define closed-loop noises, inherently coherent with the system and necessary for the fictitious identification procedure. Finally it requires to implement a more sophisticated PRABI algorithm because of the correlation between state and input closed-loop noises. A satellite example illustrates the main results.

In this paper, similar to the structured singular value method, necessary and sufficient condition is given for robust stability of SISO systems under both plant and controller perturbations. And a new Linear Matrix Inequality (LMI) based controller design method is presented. There is some conservatism for controller design, but this conservatism is less than the conservatism caused by the traditional method dealing with the mixed sensitivity problem.

The real stability radius for perturbed linear neutral delay systems with a single delay is investigated. We present the corresponding readily computable formulae with respect to an arbitrary stability region in the complex plane. The results are further extended to the case of linear neutral delay systems with multiple delays.

The real stability radii for perturbed linear discrete time-delay systems are investigated. We present the corresponding readily computable formulae with respect to a D-stability region in the complex plane.

Several robustness problems such as stability and performance robustness analysis of feedback systems and robust design of control systems in presence of nonlinear parametric perturbations can be solved by means of algorithms based on interval mathematic computation. Some of the main algorithms available in the literature are presented and their efficiency is tested on some examples of robustness analysis and design of control systems.

The difficulty involved in characterizing industrial processes with reliable parametrized models, and their generally variable, non-linear behavior, makes it necessary to consider the robustness of controlled processes as a key aspect in the design of control systems. In this paper a useful method is presented for analyzing the robust stability of processes with structured perturbations in their model's parameters. The process controllers considered must have a linear structure and fixed parameters This method has been implemented with specific software, called ANAGRO, which makes it possible to graphically observe whether there exists any risk of instability in the controlled process, enables graphical comparison of various PID controllers, and aids in selecting the most robust one. ANAGRO also provides a index of the robustness of various controllers for the same process, and allows the analysis of the relative stability (minimum damping value) of the system