Parameter-dependent adaptive <i>H</i>_∞ control design for a class of linear parameter-varying systems using polynomially parameter-dependent quadratic functions

This paper presents a new technique to design a parameter-dependent adaptive H ∞ control for a class of linear parameter-varying (LPV) systems. It is assumed that the statespace matrices affinely depend on parameters that are not measurable in real-time for the control process. By introducing a Hamiltonian-Jacobi-Isaac (HJI) function and using the vector projection method, a sufficient condition is first established for the stability analysis problem in terms of a parameter-dependent linear matrix inequality (LMI). Then, by means of the polynomially parameter-dependent quadratic (PPDQ) functions, a parameter-independent LMI-based condition is derived, which enables an explicit expression to be found of the parameter-dependent adaptive H ∞ control that guarantees both robust asymptotic stability and a prescribed level of disturbance attenuation for the system. Two numerical examples are given to illustrate the applicability of the proposed design approach.