Using the notion of exponential QSR-dissipativity <i>(i.e., dissipativity with respect to a quadratic supply rate given in terms real matrices Q, S,R)</i>, this article presents necessary and sufficient conditions for stabilizability nonlinear systems by linear static output feedback (SOF). It is shown that, under mild assumptions, stabilization closed-loop system around origin equivalent plant. Furthermore, whereas strict only SOF asymptotic stabilization, it proved be full state control....

In this technical note, we study the relations between local stabilizability of a class input-affine discrete-time nonlinear systems and their Quadratic-Supply-Rate (QSR)-dissipativity properties. Focusing on by linear Static Output Feedback (SOF), derive several sufficient conditions for Lyapunov based QSR-dissipativity. A closed-form expression SOF stabilizing gain is derived from QSR matrices. Additionally, prove that necessity also holds in some special cases. The QSR-dissipativity-based...

This technical note presents a proof of the equivalence between strict passivity linear time-invariant (LTI) controllable and observable systems positive realness their transfer function matrices, where direct feedthrough D is possibly non-zero matrix. Although both properties guarantee asymptotic stability, former time domain condition latter frequency concept. A numerical example illustrates our main results.

In this work we deal with the asymptotic stabilization problem of polynomial (and rational) input-affine systems subject to parametric uncertainties. The linear static output feedback (SOF) control synthesis is handled, having as a prerequisite differential algebraic representation (DAR) plant. Using property strict QSR-dissipativity, theFinsler's Lemma and notion annihilators introduce new dissipativity-based strategy for robust which determines gain by solving simple semidenite program on...

In this note, the problem of data-driven saturated state feedback design for polynomial nonlinear systems is solved by means a sum-of-squares (SOS) approach. This new strategy combines recent results in dissipativity theory and control using noisy input-state data. SOS optimization employed work controller to deliver an estimate closed-loop domain attraction under feedback. Numerical examples allow reader verify usefulness our strategy, which first literature provide dissipativity-based...

This paper presents a new controller design framework for nonlinear feedback systems using passivity indices. These indices measure the level of system and can be used to set lower bounds parameters stabilizing controller. We provide systematic way designing dynamic output based on matrix condition plant dynamics its Instead demanding solution partial differential equations derivation Casimir functions, as it is case most control by interconnection methods, our strategy relies solely...

This work presents a new controller design technique for asymptotic stabilization of nonlinear systems using passivity indices. The aforementioned indices measure the level system and we address question how to use this information dynamic output feedback that stabilizes closed-loop at given equilibrium. As full state is not always available feedback, measurable has be used. main contribution paper consists systematic way determining stabilizing based on plant sum squares (SOS) relaxations....

Recently, a new strategy for local analysis of passivity indices and its application output feedback asymptotic stabilization nonlinear systems was proposed [2]. Polynomial input-affine were considered sum squares (SOS) techniques employed estimating domain in which the are valid stability is guaranteed. Though simple useful, method still demands improvements, as estimates obtained can be quite conservative. In this context, work applies Finsler's Lemma notion linear annihilators enlarging...

In the field of closed-loop stabilization linear systems under saturated state feedback, question whether a sector-based condition or convex hull approach provides largest invariant ellipsoid as an estimate system domain attraction has been drawing great interest. This work presents proof that, regardless input size, fulfilling popular for feedback design, in fact, implies feasibility well-known polytopic obtained through representation input, resulting same contractively region asymptotic...

This note deals with the static output feedback stabilization problem of linear time-invariant (LTI) systems, one most relevant open problems in field control theory. We present a new sufficient matrix inequality (LMI) condition to test stabilizability by feedback. The notion passivity indices, as measure level system, is employed. Unlike methods currently available literature, our LMI non iterative and does not rely on similarity transformations, allowing for straightforward determination...

In this note, the problem of data-driven saturated state feedback design for polynomial nonlinear systems is solved by means a sum-of-squares (SOS) approach. This new strategy combines recent results in dissipativity theory and control using noisy input-state data. SOS optimization employed work controller to deliver an estimate closed-loop domain attraction under feedback. Numerical examples allow reader verify usefulness our strategy, which first literature provide datadriven...

Using a new set of semidefinite constraints called recurrent dissipativity-based inequalities (DBIs), this letter presents an iterative procedure to design polynomial feedback control laws for nonlinear systems, let it be static state or linear output (SOF) controller one needs determine. In addition that, the problem SOF time-invariant (LTI) systems is solved as well. case we use sum-of-squares (SOS) programming and provide estimate closed-loop domain attraction. LTI models, matrix (LMIs)...

This paper deals with robust static output feedback (SOF) stabilization of linear time-invariant (LTI) systems transient performance. The proposed approach considers uncertainties on the system matrices and does not impose any constraints matrix. We use definition strict QSR-dissipativity to formulate new sufficient conditions in form matrix inequalities (LMIs) for asymptotic stabilization. One main advantages developed strategy is that it provides a solution design non-interactive manner....

This paper proposes the design of gain-scheduled static output feedback controllers for stabilization continuous-time linear parameter-varying systems with ℒ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -gain performance. The system is transformed into form a differential-algebraic representation which allows dealing broad class whose matrices present rational or polynomial dependence on parameter. proposed approach uses definition...

This work presents a proof that the existence of sum squares (SOS) decomposition for closed-loop (asymptotic) stability condition valid around origin is equivalent, input-affine polynomial systems, to an SOS certificate strict dissipation inequality subject certain equality constraint. In addition, new sufficient feedback asymptotic stabilization nonlinear systems nonzero equilibria proposed using notion equilibrium-independent dissipativity (EID). Then, this applied specifically. It proved...

In this paper, the feedback stabilization problem of nonlinear stochastic systems driven by Wiener processes is addressed. It shown that existence a control Lyapunov function guarantees exponential mean square zero solution linear static output (SOF), under certain circumstances, equivalent to dissipativity plant. Quadratic supply rates are proved be general enough establish equivalence. Necessary and sufficient dissipativity-based conditions for asymptotic in probability via full state also...

This note is concerned with the presentation of new delay-dependent dissipativity-based convex conditions (expressed in form linear matrix inequalities) for design static output feedback (SOF) stabilizing gains open-loop unstable discrete-time systems input time-varying delays. A modified definition QSR-dissipativity combined use Lyapunov-Krasovskii functionals as storage functions and application Finsler's Lemma lead to gathering non-interactive conditions. We show that, differently from...

In this work, we propose a new approach for the robust static output feedback (SOF) stabilization of linear time-invariant (LTI) systems with transient performance. Recently published non-convex necessary and sufficient conditions SOF stabilizability LTI are leveraged to obtain convex which have benefit being numerically tractable. Here, an adaption recently developed iterative algorithm matrix inequalities (LMIs) that conveniently solved using SDP tools. Numerical examples highlight...