Analyse the stability of the following dynamical systems by using Lyapunov theory. All bold small letters...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Analyse the stability of the following dynamical systems by using Lyapunov theory. All bold small letters (e.g., v) are assumed to be column vectors. Are these systems stable, asymptotically stable, or unstable? Analytically demonstrate it. 2) y + y = u where the control input is defined as u = - 3) w = -AT Aw -5(y- yd), for yd as a desired constant target where A € Rmxn, for m > n, is a "short and fat" matrix with full-row rank. 4) x = -x³ - (x - x²) where x is a constant scalar. 5) s = ks where k > 0 is a constant scalar. Analyse the stability of the following dynamical systems by using Lyapunov theory. All bold small letters (e.g., v) are assumed to be column vectors. Are these systems stable, asymptotically stable, or unstable? Analytically demonstrate it. 2) y + y = u where the control input is defined as u = - 3) w = -AT Aw -5(y- yd), for yd as a desired constant target where A € Rmxn, for m > n, is a "short and fat" matrix with full-row rank. 4) x = -x³ - (x - x²) where x is a constant scalar. 5) s = ks where k > 0 is a constant scalar.
Expert Answer:
Answer rating: 100% (QA)
Solution 2 The dynamical system is described by the equation y y u where u is the control input To use Lyapunov theory we need to define a Lyapunov fu... View the full answer
Related Book For
Fundamentals of Thermal-Fluid Sciences
ISBN: 978-0078027680
5th edition
Authors: Yunus A. Cengel, Robert H. Turner, John M. Cimbala
Posted Date:
Students also viewed these civil engineering questions
-
You are to design a rotating cylindrical axle to lift 800-N buckets of cement from the ground to a rooftop 7S.0 m above the ground. The buckets will be attached to a hook on the free end of a cable...
-
You are required to design a speed gearbox made up of spur gears with three stages of speed reduction apart from the belt-pulley stage) to impart a total of 20 spindle speeds with 5 speeds in stage...
-
You are to design a packed column to absorb C02 from air into fresh, dilute-caustic solution. The entering air contains 3 mol% C02, and a 97% recovery of C02 is desired. The gas flow rate is 5,000...
-
Is there more to marketing than building product and brand awareness than what people discuss? How do marketing managers and executives manage consistent messaging across cultures?
-
Explain each of the following concepts: a. Correlation matrix b. R2 c. Multicollinearity d. Residual e. Dummy variable f. Stepwise regression
-
Why might it be helpful to export data from an Access database to an HTML file?
-
The 2005 comparative balance sheet and income statement of Get Wired, Inc., follow on the next page. Get Wired, Inc., had no noncash investing and financing transactions during 2005. During the year,...
-
A refrigerator used by a meat processor has a cost of $120,000, an estimated residual value of $14,000, and an estimated useful life of 16 years. What is the amount of the annual depreciation...
-
When large corporations are expanding and looking for new locations across the country to develop a presence, they examine many aspects of finding a new location from many angles. They want a...
-
A construction company wants to determine the optimal replacement policy for the earth mover it owns. The company has a policy of not keeping an earth mover for more than five years, and has...
-
Image transcription text recommend no reply be sent. 2. You are flying a corporate turboprop from Miami to Chicago under Instr (IF R.). Your course takes you through a cold front with imbedded...
-
How does the concept of moral relativism intersect with discussions surrounding ethical behavior in diverse cultural contexts ?
-
If the Rydberg energy is 1 3 . 6 eV , what is the wavelength of light emitted when the electron drops from confined level n = 2 to n = 1 ?
-
Propose a NEW operating systems. The NEW operating systems can be based on Windows or Unix/Linux or Mobile OS or independent based platform. Provide details and justifications of your NEW operating...
-
A solid wood door 1.50 m wide and 5.00 m high is hinged along one side and has a total mass of 42.0 kg . Initially open and at rest, the door is struck at its center by a handful of sticky mud with...
-
How does organizational culture serve as a dynamic system of shared values, beliefs, and norms that shape the behaviors, decisions, and perceptions of individuals within the organizational context ?
-
What did VW do well, and not-so-well in managing their crisis? Reflect on the five practical steps in Chapter 6 on "Managing Business Crises" and identify the areas where, according to the expert in...
-
Show that every group G with identity e and such that x * x = e for all x G is abelian.
-
A rotating viscometer consists of two concentric cylindersa stationary inner cylinder of radius R i and an outer cylinder of inside radius R o rotating at angular velocity (rotation rate) Ï o ....
-
In a geothermal power plant, the used geothermal water at 80°C enters a 15-cm-diameter and 400-m-long uninsulated pipe at a rate of 8.5 kg/s and leaves at 70°C before being reinjected back to...
-
What does the logarithmic mean temperature difference represent for flow in a tube whose surface temperature is constant? Why do we use the logarithmic mean temperature instead of the arithmetic mean...
-
Name four disruptive business models and describe what they offer to their customers.
-
How is IT contributing to the success of the on-demand and shared economies?
-
What are the key strategic and tactical questions that determine an organizations profitability and management performance?
Study smarter with the SolutionInn App