Fixed order multivariable controller synthesis: A new algorithm

We consider the synthesis of a fixed order or fixed structure multivariable feedback controller C, parametrized by a design vector x, for a plant P, containing a vector p of uncertain parameters. The characteristic polynomials of such systems contain coefficients which depend polynomially on x and p. Using results on sign definite decomposition we develop a 4-polynomial stability test that gives a sufficient condition for stability of the family of closed loop systems that result when x and p vary over prescribed boxes. This test is reminiscent of Kharitonov¿s theorem, even though the family of polynomials considered here is certainly not restricted to be interval or even convex. Moreover this result is tight in the sense that the test does reduce to Kharitonov¿s theorem for the special case of interval polynomials. Using this criterion recursively and modularly we design an algorithm to determine sets of controllers that stabilize the family of uncertain plants. Examples and future research directions are provided.