Observer based minimum variance control of uncertain piecewise affine systems subject to additive noise

In this paper, a class of uncertain piecewise affine (PWA) systems, subject to system and measurement additive noises is studied. The additive noise signals considered here do not vanish at the equilibrium and the uncertainties are norm bounded. The problem of minimizing the bound on the variance of the steady response of uncertain PWA systems, by means of a hybrid observer–controller, is formulated as an optimization problem subject to a number of constraints in the form of matrix inequalities. The derived constraints are obtained by considering a piecewise quadratic Lyapunov function in combination with the general stability conditions regarding the existence of an upper stochastic bound on the steady state variance for a class of stochastic hybrid systems (SHS). Then the uncertain PWA approximation of a practical system with nonlinear dynamics is presented considering system and measurement noises. The uncertainties arise in the form of the difference between the actual nonlinear dynamics and the PWA approximation. Utilizing the introduced methods, a hybrid observer–controller is designed and implemented on the nonlinear system to demonstrate the effectiveness of the proposed controller design procedure.