Gain Scheduling using Time-varying Kalman Filter for a class of LPV Systems ⋆

Current gain-scheduling approaches only assure stability when the underlying parameter varies sufficiently slowly, and hence stable closed-loop is not guaranteed for more general (i.e. faster) parameter variations. Shamma and Athans (1992) provides a solution to overcome this by computing Riccati Differential Equation (RDE) online for the current parameter value with the offline Algebraic Riccati Equation (ARE) solutions for every parameter value, which is computationally demanding. This paper achieves a very significant simplification, by showing how only a finite number of AREs need be used and the online RDE solutions can be computed by table look-up and matrix inversion. In simulations the method yields results indistinguishable from those achieved in Shamma and Athans (1992).