Regulator problem for uncertain linear discrete-time systems with constrained control

A necessary and sufficient condition to test the robustness of a regulator of uncertain linear systems with constrained control is given. The candidate regulator for this test is that stabilizing nominal systems. An illustrative example is also given.     

LMI-Based Approach for Output-Feedback Stabilization for Discrete-Time Takagi--Sugeno Systems

Static output-feedback stabilizing controllers for nonlinear systems represented by discrete-time Takagi--Sugeno fuzzy models are studied. The main result concerns the stabilization based on the parallel distributed compensation (PDC) approach. Sufficient conditions are provided for quadratic and nonquadratic stability. To design static output-feedback stabilizing controllers, a numerical procedure based on the cone complementarity algorithm is given. It is shown that the relaxed conditions proposed in the nonquadratic case outperform those for the quadratic case. Two numerical examples are given to illustrate the efficiency of the proposed approach.      

On the dynamic improvement in linear constrained control discrete-time systems

In the control of linear systems with asymmetrical input constraints, larger domains of initial states can be obtained by allowing slow initial dynamics of the system in a closed loop, and making it faster during its evolution. The positive invariance concept application leads to piecewise linear constrained control laws using asymmetrical polyhedral sets.     

Stabilization of controlled positive discrete‐time T‐S fuzzy systems by state feedback control

This paper deals with sufficient conditions of asymptotic stability and stabilization for nonlinear discrete‐time systems represented by a Takagi–Sugeno‐type fuzzy model whose state variables take only nonnegative values at all times t for any nonnegative initial state. This class of systems is called positive systems. The conditions of stabilizability are obtained with state feedback control. This work is based on multiple Lyapunov functions. The results are presented in linear matrix inequalities form. A real plant is studied to illustrate this technique. Copyright © 2010 John Wiley & Sons, Ltd.     

Regulator problem for linear continuous-time delay systems withnonsymmetrical constrained control

The regulator problem is studied for linear continuous-time delay systems with nonsymmetrical constrained control. Necessary and sufficient conditions allowing the autors to obtain the largest nonsymmetrical polyhedral positively invariant with respect to (w.r.t.) the system in the closed loop are given, The case of symmetrical constrained control is obtained as a particular case     

Stabilisation and control synthesis of switching systems subject to actuator saturation

This article presents sufficient conditions for the stabilisation of switching discrete-time linear systems subject to actuator saturations. These conditions are obtained by using successively state and output feedback control laws. The obtained results are formulated in terms of linear matrix inequalities (LMIs). The saturating and non-saturating controllers are synthesised for both cases in this work. Three sets of LMIs are presented for output feedback case. Numerical examples are used to illustrate these techniques by using a linear optimisation problem subject to LMI constraints.     

Stabilisation of controlled positive delayed continuous-time systems

This article solves the stabilisation problem by output feedback control for linear continuous-time systems with delay. This technique can be applied for both positive systems and controlled positive systems (systems becoming positive in closed-loop). The synthesis of feedback controllers is solved in terms of linear programs, extending the solution also to stabilisation with bounded control and stabilisation by controllers with the memory of the delayed state. The proposed conditions do not involve the value of the delay. Some examples illustrate the proposed approach.     

Partial eigenstructure assignment problem and its application to the constrained linear problem

This article presents a new partial eigenstructure assignment method. This technique keeps the open-loop stable eigenvalues and the corresponding eigenspace unchanged. The remaining undesirable eigenvalues are replaced by other chosen values. This methodology is easy and permits to overcome some limitations encountered in the previous methods. Furthermore, our method is applied to solve the constrained control problem for linear invariants continuous-time systems. Indeed, the problem of finding a stabilising regulator matrix gain taking into account the asymmetrical control constraints is transformed to a Sylvester equation resolution. Examples are given to illustrate the obtained results.     

Constrained control of switching systems: a positive invariant approach

This paper presents conditions for the stabilization of switching discrete-time linear systems with constrained control by using a positive invariance approach. A state feedback control law is used to construct the stabilizing controller. A numerical example is presented to illustrate the technique.     

The resolution of equation XA+XBX=HX and the pole assignmentproblem

This paper deals with the resolution of equation XA+XBX=HX, which plays a fundamental rule in the design of controllers of linear systems with constrained control by the use of the recently developed concept of positive invariance. It is also shown that this equation represents a partially pole assignment problem. Such resolution allows us to build a new method, called the inverse procedure, to design these controllers