This paper is concerned with the design of state-feedback variable-structure controllers (VSCs) for a class of continuous-time switched plants. In particular, a new VSC design method based on Lyapunov-Metzler (LM) inequalities and the properties of strictly positive real (SPR) systems is suggested. The method is applied to the control of a DC-DC power converter. The performance of the resulting control system is superior to that afforded by a recently proposed alternative sliding-mode control technique. The definition of LM-SPR systems and its direct application to establish a procedure for designing the switching rule and VSC input are presented.

In some practical problems, for instance in the control systems for the suppression of vibration in mechanical systems, the state-derivative signals are easier to obtain than the state signals. New necessary and sufficient linear matrix inequalities (LMI) conditions for the design of state-derivative feedback for multi-input (MI) linear systems are proposed. For multi-input/multi-output (MIMO) linear time-invariant or time-varying plants, with or without uncertainties in their parameters, the proposed methods can include in the LMI-based control designs the specifications of the decay rate, bounds on the output peak, and bounds on the state-derivative feedback matrix K. These design procedures allow new specifications and also, they consider a broader class of plants than the related results available in the literature. The LMIs, when feasible, can be efficiently solved using convex programming techniques. Practical applications illustrate the efficiency of the proposed methods.

This paper is concerned with the design of state-feedback switched controllers for a class of uncertain nonlinear plants described by Takagi-Sugeno (T-S) fuzzy models. The proposed methodology eliminates the need to find the membership function expressions to implement the control law, which is relevant in cases where the membership function depends on uncertain parameters. The design of the switched controllers is based on a minimum-type Lyapunov function and the minimization of the time derivative of this Lyapunov function. The conditions of the new stability criterion are represented by a kind of bilinear matrix inequalities (BMIs) that has been solved by the path-following method. A numerical example and the nonlinear control design of a magnetic levitator with uncertainties illustrate the procedure.

In some practical problems, for instance in the control systems for the suppression of vibration in mechanical systems, the state-derivative signals are easier to obtain than the state signals. Necessary and sufficient LMI-based conditions for pole placement of linear systems using state-derivative feedback are proposed. Sufficient conditions for pole placement for a class of uncertain systems or systems subject to structural failures are also presented. The simulation of practical applications illustrates the efficiency of the proposed methods.

This brief proposes a new method for the identification of fractional-order transfer functions based on the time response resulting from a single step excitation. The proposed method is applied to the identification of a 3-D RC network, which can be tailored in terms of topology and composition to emulate real-time systems governed by fractional-order dynamics. The results are in excellent agreement with the actual network response, yet the identification procedure only requires a small number of coefficients to be determined, demonstrating that the fractional-order modeling approach leads to very parsimonious model formulations.