This paper addresses the consensus problem of first‐order continuous‐time multi‐agent systems over undirected graphs. Each agent samples relative state measurements in a self‐triggered fashion and ...transmits the sum of the measurements to its neighbours. Moreover, we use finite‐level dynamic quantizers and apply the zooming‐in technique. The proposed joint design method for quantization and self‐triggered sampling achieves asymptotic consensus, and inter‐event times are strictly positive. Sampling times are determined explicitly with iterative procedures including the computation of the Lambert W‐function. A simulation example is provided to illustrate the effectiveness of the proposed method.
This paper addresses the consensus problem of multi‐agent systems over undirected graphs. Each agent samples relative state measurements in a self‐triggered fashion and transmits the sum of the measurements to its neighbours. The proposed joint design method for quantization and self‐triggered sampling achieves asymptotic consensus, and inter‐event times are strictly positive.
Let
-
A
be the generator of a bounded
C
0
-semigroup
(
e
-
t
A
)
t
≥
0
on a Hilbert space. First we study the long-time asymptotic behavior of the Cayley transform
V
ω
(
A
)
:
=
(
A
-
ω
I
)
(
A
+
ω
I
...)
-
1
with
ω
>
0
. We give a decay estimate for
‖
V
ω
(
A
)
n
A
-
1
‖
when
(
e
-
t
A
)
t
≥
0
is polynomially stable. Considering the case where the parameter
ω
varies, we estimate
‖
(
∏
k
=
1
n
V
ω
k
(
A
)
)
A
-
1
‖
for exponentially stable
C
0
-semigroups
(
e
-
t
A
)
t
≥
0
. Next we show that if the generator
-
A
of the bounded
C
0
-semigroup has a bounded inverse, then
sup
t
≥
0
‖
e
-
t
A
-
1
A
-
α
‖
<
∞
for all
α
>
0
. We also present an estimate for the rate of decay of
‖
e
-
t
A
-
1
A
-
1
‖
, assuming that
(
e
-
t
A
)
t
≥
0
is polynomially stable. To obtain these results, we use operator norm estimates offered by a functional calculus called the
B
-calculus.
This paper is concerned with the decay rate of
e
A
-
1
t
A
-
1
for the generator
A
of an exponentially stable
C
0
-semigroup on a Hilbert space. To estimate the decay rate of
e
A
-
1
t
A
-
1
, we ...apply a bounded functional calculus. Using this estimate and Lyapunov equations, we also study the quantified asymptotic behavior of the Crank-Nicolson scheme with smooth initial data. A similar argument is applied to a polynomially stable
C
0
-semigroup whose generator is normal.
In this paper, we study the decay rate of the Cayley transform of the generator of a polynomially stable
C
0
-semigroup. To estimate the decay rate of the Cayley transform, we develop an integral ...condition on resolvents for polynomial stability. Using this integral condition, we relate polynomial stability to Lyapunov equations. We also study robustness of polynomial stability for a certain class of structured perturbations.
We study the sample-data control problem of output tracking and disturbance rejection for unstable well-posed linear infinite-dimensional systems with constant reference and disturbance signals. We ...obtain a sufficient condition for the existence of finite-dimensional sampled-data controllers that are solutions of this control problem. To this end, we study the problem of output tracking and disturbance rejection for infinite-dimensional discrete-time systems and propose a design method of finite-dimensional controllers by using a solution of the Nevanlinna–Pick interpolation problem with both interior and boundary conditions. We apply our results to systems with state and output delays.
Permanent-magnet synchronous motors have attracted much attention due to their high efficiency and high-torque density. For higher control performance, finite control set model predictive control ...(FCS-MPC) and continuous control set MPC (CCS-MPC) have been developed. However, the former requires high computing power, whereas inverter voltage saturation is not considered in the latter. Therefore, this study proposes an optimal current control law taking into consideration the inverter output voltage. The effectiveness of the proposed method is verified by comparison with the FCS-MPC and the standard CCS-MPC through experiments.
We analyze the robustness of the exponential stability of infinite-dimensional sampled-data systems with unbounded control operators. The unbounded perturbations we consider are the so-called ...Desch–Schappacher perturbations, which arise, e.g., from the boundary perturbations of systems described by partial differential equations. As the main result, we show that the exponential stability of the sampled-data system is preserved under all Desch–Schappacher perturbations sufficiently small in a certain sense.
We analyze the exponential stability of a class of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying ...coefficients. We approximate the coefficients by splitting space domains but take into account approximation errors during stability analysis. Using a quadratic Lyapunov function, we obtain sufficient conditions for exponential stability in terms of linear matrix inequalities.
Abstract Let $$-A$$ - A be the generator of a bounded $$C_0$$ C 0 -semigroup $$(e^{-tA})_{t \ge 0}$$ ( e - t A ) t ≥ 0 on a Hilbert space. First we study the long-time asymptotic behavior of the ...Cayley transform $$V_{\omega }(A) :=(A-\omega I) (A+\omega I)^{-1}$$ V ω ( A ) : = ( A - ω I ) ( A + ω I ) - 1 with $$\omega >0$$ ω > 0 . We give a decay estimate for $$\Vert V_{\omega }(A)^nA^{-1}\Vert $$ ‖ V ω ( A ) n A - 1 ‖ when $$(e^{-tA})_{t \ge 0}$$ ( e - t A ) t ≥ 0 is polynomially stable. Considering the case where the parameter $$\omega $$ ω varies, we estimate $$\Vert (\prod _{k=1}^n V_{\omega _k}(A))A^{-1}\Vert $$ ‖ ( ∏ k = 1 n V ω k ( A ) ) A - 1 ‖ for exponentially stable $$C_0$$ C 0 -semigroups $$(e^{-tA})_{t \ge 0}$$ ( e - t A ) t ≥ 0 . Next we show that if the generator $$-A$$ - A of the bounded $$C_0$$ C 0 -semigroup has a bounded inverse, then $$\sup _{t \ge 0} \Vert e^{-tA^{-1}} A^{-\alpha } \Vert < \infty $$ sup t ≥ 0 ‖ e - t A - 1 A - α ‖ < ∞ for all $$\alpha >0$$ α > 0 . We also present an estimate for the rate of decay of $$\Vert e^{-tA^{-1}} A^{-1} \Vert $$ ‖ e - t A - 1 A - 1 ‖ , assuming that $$(e^{-tA})_{t \ge 0}$$ ( e - t A ) t ≥ 0 is polynomially stable. To obtain these results, we use operator norm estimates offered by a functional calculus called the $$\mathcal {B}$$ B -calculus.
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