Switched adaptive control of switched nonlinearly parameterized systems with unstable subsystems

This paper investigates the problem of adaptive stabilization for a class of switched nonlinearly parameterized systems where the solvability of the adaptive stabilization problem for subsystems is unnecessary. A new switched adaptive control technique for the problem studied is set up by exploiting the generalized multiple Lyapunov functions method and the parameter separation technique. Different update laws are designed to reduce the conservativeness caused by adoption of a common update law for all subsystems. Also, the proposed technique permits removal of a common restriction in which the parameterization in the switched systems is restricted to a linear parameterization. As an application of the proposed design technique, stabilization for a class of non-triangular switched systems with nonlinear parameterization is achieved by design of adaptive controllers. Since no subsystem of such a switched system is assumed to be adaptively stabilizable, the problem under study cannot be handled by the existing methods. A two inverted pendulums as a practical example is also provided to demonstrate the effectiveness of the proposed design method.