Control And Filtering For Systems With Time-varying Nonlinear Parameters

The problems of controllers and filters design for a class of nonlinear parameter-varyingsystems are investigated by using parameter-dependent Lyapunov functions in this paper. Thisclass of nonlinear parameter-varying systems are more general than linear parameter-varyingsystems as well as polytopic systems. The main results are as follows:Part 1. This part deals with the problem of H∞filter design for a class of nonlinearparameter-varying discrete-time systems with quantized signals. The measurement signal isquantized by a static and logarithmic quantizer. The analysis conditions of stability and withH∞performance for the filtering error system are obtained by using parameter-dependentLyapunov functions. Based on these conditions and matrices relaxation technique, filteringproblem is presented in terms of a finite number of linear matrix inequalities (LMIs) , and anexplicit expression of the desired filter is also given. Finally, a numerical example is providedto demonstrate the applicability of the proposed approach.Part 2. This part investigates the H∞control problem for a class of nonlinear parameter-varying systems with time delays. Based on a homogeneous polynomial Lyapunov function, anew analysis condition is proposed for this class of systems under consideration. A solvablesu?cient condition on the H∞control problem is provided by combining the homogeneouspolynomial approach with delay-dependent method. When the degrees of the associated homo-geneous polynomial parameter-dependent matrices (HPPDM) are one, these matrices becomelinearly dependent on parameters, which has been commonly used in dealing with parameter-varying systems. The HPPDM approach is thus less conservative than the linearly parameter-dependent matrix (LPDM) approach. A numerical example is also given for illustrating theless conservatism of the obtained results.Part 3. The H∞filtering problem for a class of nonlinear parameter-varying systemsis considered by using a parameter-dependent Lyapunov function in this part. Based on thehomogeneous polynomial parameter-dependent matrix (HPPDM) approach, the earlier analysisresult is transformed into solvable condition with less conservatism. With the degree of HPPDM increasing, the less conservative condition can be obtained. Finally, the less conservatism ofthe proposed approach is demonstrated by a numerical example.