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We present an application of a new controller order reduction technique with stability and performance preservation based on linear matrix inequality optimization to an active suspension system. In this technique, the rank of the residue matrix of a proper rational approximation of a high-order H ∞ controller subject to the H∞ norm of a frequency-weighted error between the approximated controller and high-order H∞ controller is minimized. However, since solving this matrix rank minimization problem is very difficult, the rank objective function is replaced with the nuclear-norm that can be reduced to a semidefinite program, so that it can be solved efficiently. Application to the active... 

This paper considers the problem of stabilizing a class of linear time-invariant large-scale systems composed of a number of subsystems using several local dynamic output feedback controllers. For this problem, a sufficient condition on each closed-loop individual subsystem is derived under which the decentralized controller composed of the local controllers designed for individual subsystems, achieves stability for the overall system. This condition is used to convert the decentralized stabilization problem to a set of the H∞ disturbance rejection subproblems  

This paper considers the problem of stabilizing a class of linear time-invariant large-scale systems composed of a number of subsystems using several local dynamic output feedback controllers. For this problem, a sufficient condition on each closed-loop individual subsystem is derived under which the decentralized controller composed of the local controllers designed for individual subsystems, achieves stability for the overall system. This condition is used to convert the decentralized stabilization problem to a set of the H∞ disturbance rejection subproblems  

This paper presents a new decentralized control strategy for the islanded operation of a microgrid under unknown load conditions. In the islanded mode of operation, the microgrid should provide the load with a set of regulated balanced three-phase voltages. The load which is parametrically and topologically uncertain can also be unbalanced and/or nonlinear. Thus, the use of conventional control strategies results in the poor performance and even instability of the microgrid system. The proposed method assumes that the load current is a measurable disturbance signal. The robust optimal control approaches are used to design a controller to overcome the disturbances resulting from the unknown... 

This letter presents new sufficient conditions for robust Hurwitz stability of interval matrices. The proposed conditions are based on two approaches: (i) finding a common Lyapunov matrix for the interval family and (ii) converting the robust stability problem into a robust non-singularity problem using Kronecker operations. The main contribution of the letter is to derive accurate and computationally simple optimal estimates of the robustness margin and spectral bound of general interval matrices. The evaluation of the condition relies on the solutions of linear matrix inequalities (LMIs) and eigenvalue problems, both of which are solved very efficiently. The improvements gained by using... 

This paper presents a novel fault-tolerant control strategy to compensate the time-varying loss of actuators’ effectiveness. It considers intermediate situations where the fault is not determined precisely (unlike active approaches) but overall estimations about its rate and final value are available through the previous experiences and/or experiments. Based on the estimations, two upper and lower time-varying bounds on the actuators’ effectiveness are established to be exploited in the procedure of controller design. In a special case, where these bounds are constant, the method will be reduced to the conventional passive approach. Also, actuator saturation and the effects of (Formula... 

The aim of this study is to reduce the computational load in model predictive control of multi-input nonlinear systems. First, the nonlinear system which has a high number of states and inputs is decomposed into several subsystems by solving a linear integer programming problem offline. Then, the model of each subsystem is revised by considering the effect of coupling and interactions of other subsystems. Next, the robust model predictive technique based on linear matrix inequalities is employed to compute control signal for each subsystem. An industrial chemical reaction example is used to illustrate the effectiveness of the proposed method. © 2017 IEEE  

This paper introduces a new methodology for the design of fixed-order multi-objective output feedback controllers. The problem comprises a set of linear matrix inequalities and an additional rank constraint. The primary idea is to classify convex subsets of the set of rank constrained matrices in such formulations, based on which two noniterative and relatively fast methods are developed. The proposed methods require solving a convex optimization problem at each step and can be applied with any weighted summation of design objectives such as (Formula presented.) performance, (Formula presented.) performance, passivity, and regional pole assignment. Several benchmark systems with performance... 

This paper develops a stability and performance preserving controller order reduction method for linear time-invariant continuous-time single-input, single-output systems. In this method, the error between the complementary sensitivity functions of the nominal closed-loop system and closed-loop system using the reduced-order controller is converted to a frequency-weighted error between the Youla parameters of the full-order and reduced-order controllers and then the H∞norm of this error, subject to a set of linear matrix inequality constraints, is minimized. The main ideas of order reduction and stability preservation are contained in the constraints of the optimization problem. However,... 

H∞ controller order reduction with stability and performance preservation pose unique challenges to designers. In the paper, an approach for controller order reduction based on minimization of the rank of a matrix variable, subject to linear matrix inequality constraints, is presented. In this approach, the rank of a residue matrix of a high-order controller subject to the error between the loop gain of the closed-loop nominal system and the loop gain of the closed-loop system with the reduced order controller is minimized. However, since solving this matrix rank minimization problem is very difficult, the rank objective function is replaced with the nuclear-norm that can be reduced to a... 

In this paper, the stabilization of linear time-invariant systems with fractional derivatives using a limited number of available state feedback gains, none of which is individually capable of system stabilization, is studied. In order to solve this problem in fractional order systems, the linear matrix inequality (LMI) approach has been used for fractional order systems. A shadow integer order system for each fractional order system is defined, which has a behavior similar to the fractional order system only from the stabilization point of view. This facilitates the use of Lyapunov function and convex analysis in systems with fractional order 1