Active Suspension Control Using an MPC-LQR-LPV Controller with Attraction Sets and Quadratic Stability Conditions

The control of an automotive suspension system by means of a hydraulic actuator is a complex nonlinear control problem. In this work, a Linear Parameter Varying (LPV) model is proposed to reduce the complexity of the system while preserving the nonlinear behavior. In terms of control, a dual controller consisting of a Model Predictive Control (MPC) and a Linear Quadratic Regulator (LQR) is implemented. To ensure stability, Quadratic Stability conditions are imposed in terms of Linear Matrix Inequalities (LMI). Simulation results for quarter-car model over several disturbances are tested in both frequency and time domain to show the effectiveness of the proposed algorithm.

Quadratic Stabilization of Linear Uncertain Positive Discrete-Time Systems

The paper provides extended methods for control linear positive discrete-time systems that are subject to parameter uncertainties, reflecting structural system parameter constraints and positive system properties when solving the problem of system quadratic stability. By using an extension of the Lyapunov approach, system quadratic stability is presented to become apparent in pre-existing positivity constraints in the design of feedback control. The approach prefers constraints representation in the form of linear matrix inequalities, reflects the diagonal stabilization principle in order to apply to positive systems the idea of matrix parameter positivity, applies observer-based linear state control to assert closed-loop system quadratic stability and projects design conditions, allowing minimization of an undesirable impact on matching parameter uncertainties. The method is utilised in numerical examples to illustrate the technique when applying the above strategy.

A Comparison Between Robust Control Design LMIs for Grid-Connected Converters

This paper is focused on a comparison between two linear matrix inequality conditions for design of robust state feedback controllers applied for current regulation of gridconnected converters with LCL filters, operating under uncertain grid impedance at the point of common coupling. The first condition is the well known quadratic stability and the second one is the polyquadratic stability, which uses extra matrix variables. It is shown that the condition with slack variables can provide superior performance in terms of ensuring stable and suitable operation for a larger set of uncertainties.

Robust Distributed Filters Design for Discrete-time Spatially Interconnected Systems with LFT Uncertainties

In this paper, we investigate discrete-time uncertain spatially interconnected systems (USISs), where uncertainties are modeled by linear fractional transformation (LFT). First, the well-posedness, quadratic stability and contractiveness of discrete-time USISs are introduced. Second, a sufficient condition is proposed to guarantee that discrete-time USISs are well-posed, quadratically stable and contractive. Then, a more tractable condition is derived to check the well-posedness, quadratic stability and contractiveness of discrete-time USISs via a modified bilinear transformation. Besides, the robust distributed filters which inherit the structure of the plants are designed. A sufficient and necessary condition is presented to guarantee the existence of the robust distributed filters. Finally, a vehicle platoon model demonstrates the effectiveness of the proposed scheme.

Quadratic Stability of Non-Linear Systems Modeled with Norm Bounded Linear Differential Inclusions

In this article we present an ordinary differential equation based technique to study the quadratic stability of non-linear dynamical systems. The non-linear dynamical systems are modeled with norm bounded linear differential inclusions. The proposed methodology reformulate non-linear differential inclusion to an equivalent non-linear system. Lyapunov function demonstrate the existence of a symmetric positive definite matrix to analyze the stability of non-linear dynamical systems. The proposed method allows us to construct a system of ordinary differential equations to localize the spectrum of perturbed system which guarantees the stability of non-linear dynamical system.

Robust PID controller design with H2 performance: Descriptor systems approach

The paper deals with the problem to obtain robust PID controller design procedure to linear time invariant descriptor uncertain polytopic systems using descriptor system stability theory and H2 criterion approach in the form of quadratic cost function. In the frame of Lyapunov function, H2 quadratic cost function and Bellman-Lyapunov equation the obtained designed novel procedure guarantees the robust properties of closed-loop system with parameter dependent quadratic stability/quadratic stability. In the obtained design procedure, the designer could use controller with different structure like as P, PI, PID, PI-D. For PI-D controllers D-part feedback the designer could choose any available output/state derivative variables of real systems. The effectiveness of the obtained results is demonstrated on the randomly generated examples.