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We consider a class of nonlinear systems which are absorbable in a linear differential inclusion (LDI), namely whose trajectories are a subset of an LDI. We show than if such an LDI is stabilizable via a linear compensator then a parametrization of all non-linear stabilizing compensators can be derived. The proposed parametrization is simple and the result is constructive. A meaningful application of the parametrization to the switching compensator problem is proposed.

We consider a plant the dynamics of which switch among a family of systems. Each of these systems has a single stable equilibrium point. We assume that a constraint region for the state is assigned and we consider the problem of finding suitable limitations on the commutation speed in order to avoid constraints violations, even in the absence of state measurements. We introduce the concepts of modal and transition dwell times which lead to the definition of dwell time vector and dwell time graph (represented by a proper matrix), respectively. The former imposes a minimum permanence time on a discrete mode before commuting, the latter imposes the minimum permanence time on the current mode before switching to a specific new one. Both dwell time vector and dwell time graph can be computed via set-theoretic techniques. When the systems share a single equilibrium state, stability can be assured as a special case. Finally, under the assumption of affine dynamics, non-conservative values are achieved.

The paper deals with the stabilizability of linear plants whose parameters vary with time in a compact set. First, necessary and sufficient conditions for the existence of a linear gain-scheduled stabilizing compensator are given. Next, it is shown that, if these conditions are satisfied, any compensator transfer function depending on the plant parameters and internally stabilizing the closed-loop control system when the plant parameters are constant, can be realized in such a way that the closed-loop asymptotic stability is guaranteed under arbitrary parameter variations. To this purpose, it is preliminarily proved that any transfer function that is stable for all constant parameters values admits a realization that is stable under arbitrary parameter variations (linear parameter-varying (LPV) stability). Then, the Youla-Kucera parametrization of all stabilizing compensators is exploited; precisely, closed-loop LPV stability can be ensured by taking an LPV stable realization of the Youla-Kucera parameter. To find one such realization, a reasonably simple and general algorithm based on Lyapunov equations and Cholesky's factorization is provided. These results can be exploited to apply linear time-invarient design to LPV systems, thus achieving both pointwise optimality (or pole placement) and LPV stability. Some potential applications in adaptive control and online tuning are pointed out.

In this paper, the class of real Lyapunov functions induced by complex polytopes is investigated. Such polytopes are in some sense the extension of real polytopes to the complex space, but have some peculiar aspects which might be relevant for the solution of constrained and/or robust control problems. In detail, analysis and synthesis results (which rely on real polytopes) for a class of linear uncertain systems are extended to the complex case. A relevant contribution of this new extensions is that of showing that the stabilizability (stability) conditions imply that the projection (projection and intersection) on the real space of such complex polytopes are level sets of control Lyapunov functions, say they can be used to derive a stabilizing control law.

In this paper, a software package for computing the maximal invariant set of constrained linear parameter varying (LPV) systems is presented. The theoretical details at the basis of the proposed algorithm are first briefly illustrated along with the extensions which allow to deal with systems affected by disturbances and different kinds of uncertainty. Then, the algorithm is presented together with some comments on its actual implementation.

The paper deals with the problem of characterizing a class of second-order three-parameter controllers (including PID and lag/lead) satisfying given H/sub /spl infin// closed-loop specifications. Simple geometric considerations allow us to easily prove and extend to a larger class of compensators some recent results on PID control [A. Datta et al., 2000], [M.T. Ho, December 2001]. Specifically it is shown that, given the value of one parameter: (i) the region of the plane defined by the other two parameters where the considered H/sub /spl infin// constraint is satisfied, consists of the union of convex sets, (ii) the closed-loop pole distribution is the same for all point inside each set and, (iii) a bound on the number of these sets is supplied by the pancake-cutting formula. An example illustrates how the method can be applied to design a PID controller in the case of bounded sensitivity.

Solving a continuous-time optimal control problem under state and control constraints is known to be a very hard task. In this note, we propose a suboptimal solution based on the Euler auxiliary system (EAS). We show that we can determine a continuous-time stabilizing control whose cost not only converges to the optimal as the EAS time parameter vanishes, but it is also upper bounded by the discrete-time cost, no matter how such a parameter is chosen. In particular, continuous-time linear problems with convex cost can be solved by considering a fictitious receding-horizon scheme. Both stability and constraints satisfaction are guaranteed for the continuous-time system. This scheme turns out to be very useful when, due to unstable or poorly damped dynamics, the digital implementation of the control requires a very small (virtually zero) sampling time, since the "time parameter" of the EAS can be much greater than the sampling time, without compromising stability, with a strongly reduced computational burden.

It has been recently shown that for the problem of optimal rejection of persistent disturbances using full-state feedback, static nonlinear controllers can recover the performance level achieved by any linear dynamic controller. In this paper we complement these results by showing that for this problem nonlinear dynamic time-varying finite dimensional, possibly discontinuous, compensators do not offer any advantage over memoryless time invariant nonlinear-compensators. Moreover, we show that the best possible (over the set of all stabilizing controllers) disturbance rejection can be achieved by using globally Lipschitz piecewise-linear controllers.

We face the problem of stabilizing Linear Parameter Varying systems by means of Gain Scheduling Control. This technique consists on designing a controller which is able to update its parameters on-line according to the variations of the plant parameters. We first consider the state feedback case and we show a design procedure based on the construction of a Lyapunov function for discrete-time LPV systems in which the parameter variations are affine and occur in the state matrix only Then we show that this procedure has a dual version which leads to the construction of a linear gain scheduling observer. The two procedures may be combined to derive an observer-based gain scheduling compensator.