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Output feedback controller synthesis for piecewise-affine systems with multiple equilibria

This work builds on the stability analysis of piecewise-affine systems reported by Hassibi et al. (1998) and extends it to obtain a new synthesis tool for output feedback controllers. The proposed technique relies on formulating the search for a piecewise-quadratic Lyapunov function and a piecewise-affine controller as a bilinear matrix inequality. This can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities which can be solved numerically and very efficiently. A key point in this design technique is that it can be used to design controllers with different structures depending on the number of constraints that are added. In particular, it is shown that a controller with the structure of a regulator and estimator can be designed so that switching based on state estimates rather than on the output can be performed. It is also shown that many other desired features can be included in the design. Furthermore, the applicability of this design method to systems with multiple equilibrium points is shown in simulation examples.