Conference Paper

# On ℋ∞ control with multiple packet dropouts: Dealing with repeated scalar nonlinearities

Coll. of Electr. & Inf. Eng., Daqing Pet. Inst., Daqing, China

DOI: 10.1109/CDC.2009.5400059 Conference: Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on Source: IEEE Xplore

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**ABSTRACT:**This paper is concerned with the problem of H <sub>infin</sub> fuzzy filtering of nonlinear systems with intermittent measurements. The nonlinear plant is represented by a Takagi-Sugeno (T-S) fuzzy model. The measurements transmission from the plant to the filter is assumed to be imperfect, and a stochastic variable satisfying the Bernoulli random binary distribution is utilized to model the phenomenon of the missing measurements. Attention is focused on the design of an H <sub>infin</sub> filter such that the filter error system is stochastically stable and preserves a guaranteed H <sub>infin</sub> performance. A basis-dependent Lyapunov function approach is developed to design the H <sub>infin</sub> filter. By introducing some slack matrix variables, the coupling between the Lyapunov matrix and the system matrices is eliminated, which greatly facilitates the filter-design procedure. The developed theoretical results are in the form of linear matrix inequalities (LMIs). Finally, an illustrative example is provided to show the effectiveness of the proposed approach.IEEE Transactions on Fuzzy Systems 05/2009; · 5.48 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, the robust H infinity control problem is considered for a class of networked systems with random communication packet losses. Because of the limited bandwidth of the channels, such random packet losses could occur, simultaneously, in the communication channels from the sensor to the controller and from the controller to the actuator. The random packet loss is assumed to obey the Bernoulli random binary distribution, and the parameter uncertainties are norm-bounded and enter into both the system and output matrices. In the presence of random packet losses, an observer-based feedback controller is designed to robustly exponentially stabilize the networked system in the sense of mean square and also achieve the prescribed H infinity disturbance-rejection-attenuation level. Both the stability-analysis and controller-synthesis problems are thoroughly investigated. It is shown that the controller-design problem under consideration is solvable if certain linear matrix inequalities (LMIs) are feasible. A simulation example is exploited to demonstrate the effectiveness of the proposed LMI approach.IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics) 09/2007; 37(4):916-24. · 3.24 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper provides complete results on the filtering problem for a class of nonlinear systems described by a discrete-time state equation containing a repeated scalar nonlinearity as in recurrent neural networks. Both induced l<sub>2</sub> and generalized H<sub>2</sub> indexes are introduced to evaluate the filtering performance. For a given stable discrete-time systems with repeated scalar nonlinearities, our purpose is to design a stable full-order or reduced-order filter with the same repeated scalar nonlinearities such that the filtering error system is asymptotically stable and has a guaranteed induced l<sub>2</sub> or generalized H<sub>2</sub> performance. Sufficient conditions are obtained for the existence of admissible filters. Since these conditions involve matrix equalities, the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities, which can be readily solved by using standard numerical software. If these conditions are feasible, a desired filter can be easily constructed. These filtering results are further extended to discrete-time systems with both state delay and repeated scalar nonlinearities. The techniques used in this paper are very different from those used for previous controller synthesis problems, which enable us to circumvent the difficulty of dilating a positive diagonally dominant matrix. A numerical example is provided to show the applicability of the proposed theories.IEEE Transactions on Signal Processing 12/2005; · 2.81 Impact Factor

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